P1.T2. Quantitative Analysis

Practice questions for Quantitative Analysis: Econometrics, MCS, Volatility, Probability Distributions and VaR (Intro)

Sort By:
Title
Replies Views
Last Message ↓
  1. Suzanne Evans

    P1.T2.203. Skew and kurtosis (Stock & Watson)

    Thank you, David.
    Thank you, David.
    Thank you, David.
    Thank you, David.
    Replies:
    6
    Views:
    237
  2. Suzanne Evans

    P1.T2.217. Regression coefficients (Stock & Watson)

    Hi @luccacerf Yes, exactly. You are correct that the critical t-value at one-tailed 95% confidence with 2 d.f. is 4.30 per (just using Excel) = T.INV(97.5%, 2) = 4.30, but we'd have 48 - 2 = 46 df, such that T.INV(97.5%, 46) = 2.013 or T.INV.2T(5%, 46) = 2.013 is the two-tailed 95.0% critical value. And for n > 30, we can safely approximate this with the standard normal's analogous 1.96...
    Hi @luccacerf Yes, exactly. You are correct that the critical t-value at one-tailed 95% confidence with 2 d.f. is 4.30 per (just using Excel) = T.INV(97.5%, 2) = 4.30, but we'd have 48 - 2 = 46 df, such that T.INV(97.5%, 46) = 2.013 or T.INV.2T(5%, 46) = 2.013 is the two-tailed 95.0% critical value. And for n > 30, we can safely approximate this with the standard normal's analogous 1.96...
    Hi @luccacerf Yes, exactly. You are correct that the critical t-value at one-tailed 95% confidence with 2 d.f. is 4.30 per (just using Excel) = T.INV(97.5%, 2) = 4.30, but we'd have 48 - 2 = 46 df, such that T.INV(97.5%, 46) = 2.013 or T.INV.2T(5%, 46) = 2.013 is the two-tailed 95.0% critical...
    Hi @luccacerf Yes, exactly. You are correct that the critical t-value at one-tailed 95% confidence with 2 d.f. is 4.30 per (just using Excel) = T.INV(97.5%, 2) = 4.30, but we'd have 48 - 2 = 46...
    Replies:
    11
    Views:
    193
  3. Nicole Seaman

    P1.T2.312. Mixture distributions

    Just to add a few more thoughts, the exam "could" ask you to use an obscure level of significance which would require you to retrieve a value from a z table. If this was the case, the exam would provide a snippet of the respective region of the z table. (I would add that this is a totally reasonable question in my mind). Also, memorizing the most common z's will help you but I don't think...
    Just to add a few more thoughts, the exam "could" ask you to use an obscure level of significance which would require you to retrieve a value from a z table. If this was the case, the exam would provide a snippet of the respective region of the z table. (I would add that this is a totally reasonable question in my mind). Also, memorizing the most common z's will help you but I don't think...
    Just to add a few more thoughts, the exam "could" ask you to use an obscure level of significance which would require you to retrieve a value from a z table. If this was the case, the exam would provide a snippet of the respective region of the z table. (I would add that this is a totally...
    Just to add a few more thoughts, the exam "could" ask you to use an obscure level of significance which would require you to retrieve a value from a z table. If this was the case, the exam would...
    Replies:
    43
    Views:
    837
  4. PortoMarco79

    Miller, Chapter 2 video: Probabilities

    Amazing response @David Harper CFA FRM . Thanks so much.
    Amazing response @David Harper CFA FRM . Thanks so much.
    Amazing response @David Harper CFA FRM . Thanks so much.
    Amazing response @David Harper CFA FRM . Thanks so much.
    Replies:
    4
    Views:
    26
  5. Fran

    P1.T2.307. Skew and Kurtosis (Miller)

    3rd central moment = ((1-0.05)^3)*5% + ((0-0.05)^3)*95% = 4.2750% 4th central moment = ((1-0.05)^4)*5% + ((0-0.05)^4)*95% = 4.0731% Note that these are central moments and NOT standardized central moments - the standardized central moments are divided by sigma ^ n where n = 3 for skewness (=3rd central moment) and n = 4 for kurtosis (=4th central moment)
    3rd central moment = ((1-0.05)^3)*5% + ((0-0.05)^3)*95% = 4.2750% 4th central moment = ((1-0.05)^4)*5% + ((0-0.05)^4)*95% = 4.0731% Note that these are central moments and NOT standardized central moments - the standardized central moments are divided by sigma ^ n where n = 3 for skewness (=3rd central moment) and n = 4 for kurtosis (=4th central moment)
    3rd central moment = ((1-0.05)^3)*5% + ((0-0.05)^3)*95% = 4.2750% 4th central moment = ((1-0.05)^4)*5% + ((0-0.05)^4)*95% = 4.0731% Note that these are central moments and NOT standardized central moments - the standardized central moments are divided by sigma ^ n where n = 3 for skewness (=3rd...
    3rd central moment = ((1-0.05)^3)*5% + ((0-0.05)^3)*95% = 4.2750% 4th central moment = ((1-0.05)^4)*5% + ((0-0.05)^4)*95% = 4.0731% Note that these are central moments and NOT standardized...
    Replies:
    21
    Views:
    632
  6. Nicole Seaman

    P1.T2.314. Miller's one- and two-tailed hypotheses

    Hi @hellohi It's called linear interpolation, please see And hopefully my picture below will help. Your table only gives us values at 20% and 15%, but we want the value associated with 16.36%. Visually, we want the (unseen) value in the yellow cell, which is (so to speak) directly below the 16.36%. This: (16.36% - 20.00%)/(15.00% - 20.00%) = 0.728 gives us the fraction of green to blue...
    Hi @hellohi It's called linear interpolation, please see And hopefully my picture below will help. Your table only gives us values at 20% and 15%, but we want the value associated with 16.36%. Visually, we want the (unseen) value in the yellow cell, which is (so to speak) directly below the 16.36%. This: (16.36% - 20.00%)/(15.00% - 20.00%) = 0.728 gives us the fraction of green to blue...
    Hi @hellohi It's called linear interpolation, please see And hopefully my picture below will help. Your table only gives us values at 20% and 15%, but we want the value associated with 16.36%. Visually, we want the (unseen) value in the yellow cell, which is (so to speak) directly below the...
    Hi @hellohi It's called linear interpolation, please see And hopefully my picture below will help. Your table only gives us values at 20% and 15%, but we want the value associated with 16.36%....
    Replies:
    18
    Views:
    309
  7. Nicole Seaman

    P1.T2.602. Bootstrapping (Brooks)

    a GARCH process is covered in the readings.... Simulations are used to produce samples from distributions that are not parametric or not in "closed form" or, perhaps better, simulations can be used to generate samples from parametric distributions when actual samples are difficult to obtain! Imagine a simulation of earthquakes or flood levels or survival in space.....
    a GARCH process is covered in the readings.... Simulations are used to produce samples from distributions that are not parametric or not in "closed form" or, perhaps better, simulations can be used to generate samples from parametric distributions when actual samples are difficult to obtain! Imagine a simulation of earthquakes or flood levels or survival in space.....
    a GARCH process is covered in the readings.... Simulations are used to produce samples from distributions that are not parametric or not in "closed form" or, perhaps better, simulations can be used to generate samples from parametric distributions when actual samples are difficult to obtain! ...
    a GARCH process is covered in the readings.... Simulations are used to produce samples from distributions that are not parametric or not in "closed form" or, perhaps better, simulations can be...
    Replies:
    4
    Views:
    98
  8. Pam Gordon

    P1.T2.310. Probability Distributions II, Miller Chapter 4

    Hi Dave, Maybe but you have triggered me into fixing my TI settings to AOS which is awesome. Feel much more comfortable with it. It was driving me mad on the chain setting and I could not figure out what was going on. Maybe we need a forum topic with the calculator settings and shortcuts in one place. This kind of knowledge is gold dust. Thanks Brendan
    Hi Dave, Maybe but you have triggered me into fixing my TI settings to AOS which is awesome. Feel much more comfortable with it. It was driving me mad on the chain setting and I could not figure out what was going on. Maybe we need a forum topic with the calculator settings and shortcuts in one place. This kind of knowledge is gold dust. Thanks Brendan
    Hi Dave, Maybe but you have triggered me into fixing my TI settings to AOS which is awesome. Feel much more comfortable with it. It was driving me mad on the chain setting and I could not figure out what was going on. Maybe we need a forum topic with the calculator settings and shortcuts in one...
    Hi Dave, Maybe but you have triggered me into fixing my TI settings to AOS which is awesome. Feel much more comfortable with it. It was driving me mad on the chain setting and I could not figure...
    Replies:
    41
    Views:
    859
  9. Nicole Seaman

    P1.T2.502. Covariance updates with EWMA and GARCH(1,1) models

    that helps much .....thanks a lot dear deepak....;)
    that helps much .....thanks a lot dear deepak....;)
    that helps much .....thanks a lot dear deepak....;)
    that helps much .....thanks a lot dear deepak....;)
    Replies:
    18
    Views:
    445
  10. Nicole Seaman

    P1.T2.315. Miller's hypothesis tests, continued

    thanks dear @David Harper CFA FRM for your helpfull answer
    thanks dear @David Harper CFA FRM for your helpfull answer
    thanks dear @David Harper CFA FRM for your helpfull answer
    thanks dear @David Harper CFA FRM for your helpfull answer
    Replies:
    10
    Views:
    154
  11. Suzanne Evans

    P1.T2.311. Probability Distributions III, Miller

    Hi @FRMeugene it may not have a direct reference (to be honest, I don't really have time to look for the cross-referenced source in every question: many of our questions are more detailed than our summaries, so it's not productive for me. I hope you understand.) Thanks,
    Hi @FRMeugene it may not have a direct reference (to be honest, I don't really have time to look for the cross-referenced source in every question: many of our questions are more detailed than our summaries, so it's not productive for me. I hope you understand.) Thanks,
    Hi @FRMeugene it may not have a direct reference (to be honest, I don't really have time to look for the cross-referenced source in every question: many of our questions are more detailed than our summaries, so it's not productive for me. I hope you understand.) Thanks,
    Hi @FRMeugene it may not have a direct reference (to be honest, I don't really have time to look for the cross-referenced source in every question: many of our questions are more detailed than our...
    Replies:
    20
    Views:
    305
  12. David Harper CFA FRM

    L1.T2.113 Rachev's exponential

    Hi @hellohi, it is small topic, I remember it studying for part 1. It is useful for part 2, I don't think direct question would be asked on this topic. But if you liked it study it. I found it useful for my knowledge!
    Hi @hellohi, it is small topic, I remember it studying for part 1. It is useful for part 2, I don't think direct question would be asked on this topic. But if you liked it study it. I found it useful for my knowledge!
    Hi @hellohi, it is small topic, I remember it studying for part 1. It is useful for part 2, I don't think direct question would be asked on this topic. But if you liked it study it. I found it useful for my knowledge!
    Hi @hellohi, it is small topic, I remember it studying for part 1. It is useful for part 2, I don't think direct question would be asked on this topic. But if you liked it study it. I found it...
    Replies:
    10
    Views:
    170
  13. Suzanne Evans

    P1.T2.212. Difference between two means

    That was a long message to type on a phone - got kind of tired towards the end!
    That was a long message to type on a phone - got kind of tired towards the end!
    That was a long message to type on a phone - got kind of tired towards the end!
    That was a long message to type on a phone - got kind of tired towards the end!
    Replies:
    34
    Views:
    613
  14. Nicole Seaman

    P1.T2.500. Bayes theorem

    Testing Amazon link
    Testing Amazon link
    Testing Amazon link
    Testing Amazon link
    Replies:
    25
    Views:
    340
  15. David Harper CFA FRM

    L1.T2.121 Extreme value distributions

    Hi @SheldonZ Jayanthi Sankaran[/USER] is correct: extreme value distributions was previously in the FRM Part 1 (Topic 2) because the assigned distribution reading included EV, but Miller doesn't address it, so EVT currently is only to be found in FRM Part 2 (Topic 6) and nowhere in Part 1; i.e., this is on older question. For Part 1, therefore, you don't need to worry about it. For Part 2,...
    Hi @SheldonZ Jayanthi Sankaran[/USER] is correct: extreme value distributions was previously in the FRM Part 1 (Topic 2) because the assigned distribution reading included EV, but Miller doesn't address it, so EVT currently is only to be found in FRM Part 2 (Topic 6) and nowhere in Part 1; i.e., this is on older question. For Part 1, therefore, you don't need to worry about it. For Part 2,...
    Hi @SheldonZ Jayanthi Sankaran[/USER] is correct: extreme value distributions was previously in the FRM Part 1 (Topic 2) because the assigned distribution reading included EV, but Miller doesn't address it, so EVT currently is only to be found in FRM Part 2 (Topic 6) and nowhere in Part 1;...
    Hi @SheldonZ Jayanthi Sankaran[/USER] is correct: extreme value distributions was previously in the FRM Part 1 (Topic 2) because the assigned distribution reading included EV, but Miller doesn't...
    Replies:
    4
    Views:
    69
  16. David Harper CFA FRM

    L1.T2.79 Hypothesis testing

    Thank you @Nicole Manley, your link is the correct reference :) @SheldonZ I fixed it above, but it's the same as Nicole already provided. Thanks!
    Thank you @Nicole Manley, your link is the correct reference :) @SheldonZ I fixed it above, but it's the same as Nicole already provided. Thanks!
    Thank you @Nicole Manley, your link is the correct reference :) @SheldonZ I fixed it above, but it's the same as Nicole already provided. Thanks!
    Thank you @Nicole Manley, your link is the correct reference :) @SheldonZ I fixed it above, but it's the same as Nicole already provided. Thanks!
    Replies:
    10
    Views:
    140
  17. Nicole Seaman

    P1.T2.600. Monte Carlo simulation, sampling error (Brooks)

    Thank you @QuantMan2318 , nice reasoning! @ (cc [USER=27903]@Nicole Manley ) The answer is given correctly as (C) which is false. But there was a typo, consistent with the text given, it should read "In regard to true (A), (B), and (D), ..." You might notice that the explanation itemizes each of the TRUE (A), (B), and (D), specifically:
    Thank you @QuantMan2318 , nice reasoning! @ (cc [USER=27903]@Nicole Manley ) The answer is given correctly as (C) which is false. But there was a typo, consistent with the text given, it should read "In regard to true (A), (B), and (D), ..." You might notice that the explanation itemizes each of the TRUE (A), (B), and (D), specifically:
    Thank you @QuantMan2318 , nice reasoning! @ (cc [USER=27903]@Nicole Manley ) The answer is given correctly as (C) which is false. But there was a typo, consistent with the text given, it should read "In regard to true (A), (B), and (D), ..." You might notice that the explanation itemizes each...
    Thank you @QuantMan2318 , nice reasoning! @ (cc [USER=27903]@Nicole Manley ) The answer is given correctly as (C) which is false. But there was a typo, consistent with the text given, it should...
    Replies:
    4
    Views:
    108
  18. Nicole Seaman

    P1.T2.400. Fabozzi on simulations

    Hi [USER=38486]@ good question: no, the 95% confidence interval is not used because it cannot be used and is not needed. The CI is given by µ(sample) +/- (critical t)*(standard error), where (standard error) = (sample standard deviation)/sqrt(N). The 1/sqrt(N) indicates the key relationship between the length of the interval and sample size: for any given µ, critical-t, and sample standard...
    Hi [USER=38486]@ good question: no, the 95% confidence interval is not used because it cannot be used and is not needed. The CI is given by µ(sample) +/- (critical t)*(standard error), where (standard error) = (sample standard deviation)/sqrt(N). The 1/sqrt(N) indicates the key relationship between the length of the interval and sample size: for any given µ, critical-t, and sample standard...
    Hi [USER=38486]@ good question: no, the 95% confidence interval is not used because it cannot be used and is not needed. The CI is given by µ(sample) +/- (critical t)*(standard error), where (standard error) = (sample standard deviation)/sqrt(N). The 1/sqrt(N) indicates the key relationship...
    Hi [USER=38486]@ good question: no, the 95% confidence interval is not used because it cannot be used and is not needed. The CI is given by µ(sample) +/- (critical t)*(standard error), where...
    Replies:
    3
    Views:
    191
  19. David Harper CFA FRM

    L1.T2.72 Student's t distribution

    Hi SheldonZ, the df does not enter the calculation of the test statistic. Its calculated as: t = (x -mu) * sqrt(n)/ s where s is the sample standard deviation. The df comes into play at determining the critical value from the t - distribution, which you than use to compare it to the t - statistics from above, but that is not part of this exercise. I hope that helped. Addendum: Sometimes the...
    Hi SheldonZ, the df does not enter the calculation of the test statistic. Its calculated as: t = (x -mu) * sqrt(n)/ s where s is the sample standard deviation. The df comes into play at determining the critical value from the t - distribution, which you than use to compare it to the t - statistics from above, but that is not part of this exercise. I hope that helped. Addendum: Sometimes the...
    Hi SheldonZ, the df does not enter the calculation of the test statistic. Its calculated as: t = (x -mu) * sqrt(n)/ s where s is the sample standard deviation. The df comes into play at determining the critical value from the t - distribution, which you than use to compare it to the t -...
    Hi SheldonZ, the df does not enter the calculation of the test statistic. Its calculated as: t = (x -mu) * sqrt(n)/ s where s is the sample standard deviation. The df comes into play at...
    Replies:
    34
    Views:
    344
  20. David Harper CFA FRM

    P1.T2.511. First-order autoregressive, AR(1), process

    [USER=38486]@ Yes, if you look at the GARP curriculum for this year, you will see that these learning objectives are still under Topic 2, Reading 16, Diebold, Chapter 8. Thank you, Nicole
    [USER=38486]@ Yes, if you look at the GARP curriculum for this year, you will see that these learning objectives are still under Topic 2, Reading 16, Diebold, Chapter 8. Thank you, Nicole
    [USER=38486]@ Yes, if you look at the GARP curriculum for this year, you will see that these learning objectives are still under Topic 2, Reading 16, Diebold, Chapter 8. Thank you, Nicole
    [USER=38486]@ Yes, if you look at the GARP curriculum for this year, you will see that these learning objectives are still under Topic 2, Reading 16, Diebold, Chapter 8. Thank you, Nicole
    Replies:
    8
    Views:
    140
  21. David Harper CFA FRM

    L1.T2.108 Volatility forecast with GARCH(1,1)

    Hi @Tania Pereira Right, either is acceptable and, in the case of question 108.3 above, it makes a difference: the given answer is 2.363% but if we instead computed a discrete daily return (i.e., 11.052/10 - 1 = 3.83%) then the 10-day volatility forecast is 2.429%, a difference of 0.066%. That's why this older question of mine is clearly imprecise (sorry): the question needs to specify that...
    Hi @Tania Pereira Right, either is acceptable and, in the case of question 108.3 above, it makes a difference: the given answer is 2.363% but if we instead computed a discrete daily return (i.e., 11.052/10 - 1 = 3.83%) then the 10-day volatility forecast is 2.429%, a difference of 0.066%. That's why this older question of mine is clearly imprecise (sorry): the question needs to specify that...
    Hi @Tania Pereira Right, either is acceptable and, in the case of question 108.3 above, it makes a difference: the given answer is 2.363% but if we instead computed a discrete daily return (i.e., 11.052/10 - 1 = 3.83%) then the 10-day volatility forecast is 2.429%, a difference of 0.066%. That's...
    Hi @Tania Pereira Right, either is acceptable and, in the case of question 108.3 above, it makes a difference: the given answer is 2.363% but if we instead computed a discrete daily return (i.e.,...
    Replies:
    26
    Views:
    391
  22. David Harper CFA FRM

    L1.T2.70 Standard error

    Oh okay, sorry @bpdulog thank you for the heads-up! (you already copied Nicole so I won't again ....)
    Oh okay, sorry @bpdulog thank you for the heads-up! (you already copied Nicole so I won't again ....)
    Oh okay, sorry @bpdulog thank you for the heads-up! (you already copied Nicole so I won't again ....)
    Oh okay, sorry @bpdulog thank you for the heads-up! (you already copied Nicole so I won't again ....)
    Replies:
    9
    Views:
    127
  23. David Harper CFA FRM

    L1.T2.69 Sampling distribution

    Hi @bpdulog the variance is (technically) the second moment about the mean (or "around the mean";); aka, the second central moment. See As the standard deviation is the square root of variance, we can say the standard deviation is a function of the second (central) moment. The question just means to query this idea: the standard deviation of a sampling distribution is called a standard...
    Hi @bpdulog the variance is (technically) the second moment about the mean (or "around the mean";); aka, the second central moment. See As the standard deviation is the square root of variance, we can say the standard deviation is a function of the second (central) moment. The question just means to query this idea: the standard deviation of a sampling distribution is called a standard...
    Hi @bpdulog the variance is (technically) the second moment about the mean (or "around the mean";); aka, the second central moment. See As the standard deviation is the square root of variance, we can say the standard deviation is a function of the second (central) moment. The question just...
    Hi @bpdulog the variance is (technically) the second moment about the mean (or "around the mean";); aka, the second central moment. See As the standard deviation is the square root of variance,...
    Replies:
    6
    Views:
    98
  24. David Harper CFA FRM

    L1.T2.71 Central limit theorem (CLT)

    Hi @bpdulog, I see this as, we are asked to calculate the probability of more than 120 loans will default but we are not given the mean value. But we have pd and n as you know we can calculate the mean=n*p=5000*2%=100 that is mean or we can say probability of default is 100. Thank you :)
    Hi @bpdulog, I see this as, we are asked to calculate the probability of more than 120 loans will default but we are not given the mean value. But we have pd and n as you know we can calculate the mean=n*p=5000*2%=100 that is mean or we can say probability of default is 100. Thank you :)
    Hi @bpdulog, I see this as, we are asked to calculate the probability of more than 120 loans will default but we are not given the mean value. But we have pd and n as you know we can calculate the mean=n*p=5000*2%=100 that is mean or we can say probability of default is 100. Thank you :)
    Hi @bpdulog, I see this as, we are asked to calculate the probability of more than 120 loans will default but we are not given the mean value. But we have pd and n as you know we can calculate...
    Replies:
    14
    Views:
    175
  25. Nicole Seaman

    P1.T2.404. Basic Statistics

    Hi @theproman23 Yes, for observations i = {1 ....n), the sample variance is [Σ (Xi - µ)^2] /(N-1), where the numerator is the sum of squared differences (from the sample mean, µ, which i am here using to denote sample mean although it should be x-bar). Sample standard deviation is the square root of the sample variance. This question is testing logic against an understanding of these...
    Hi @theproman23 Yes, for observations i = {1 ....n), the sample variance is [Σ (Xi - µ)^2] /(N-1), where the numerator is the sum of squared differences (from the sample mean, µ, which i am here using to denote sample mean although it should be x-bar). Sample standard deviation is the square root of the sample variance. This question is testing logic against an understanding of these...
    Hi @theproman23 Yes, for observations i = {1 ....n), the sample variance is [Σ (Xi - µ)^2] /(N-1), where the numerator is the sum of squared differences (from the sample mean, µ, which i am here using to denote sample mean although it should be x-bar). Sample standard deviation is the square...
    Hi @theproman23 Yes, for observations i = {1 ....n), the sample variance is [Σ (Xi - µ)^2] /(N-1), where the numerator is the sum of squared differences (from the sample mean, µ, which i am here...
    Replies:
    2
    Views:
    158
  26. Nicole Seaman

    P1.T2.405. Distributions I

    HI @theproman23 There is no sample so there is no standard error; question 405.1 is just asking about the properties of the given distribution. To contrast, let me ask a question that does invoke the standard error (which, in this case, is the standard deviation of a sample mean not a population). Here is the alternate question just for contrast: Assume a population with mean earnings of $2.5...
    HI @theproman23 There is no sample so there is no standard error; question 405.1 is just asking about the properties of the given distribution. To contrast, let me ask a question that does invoke the standard error (which, in this case, is the standard deviation of a sample mean not a population). Here is the alternate question just for contrast: Assume a population with mean earnings of $2.5...
    HI @theproman23 There is no sample so there is no standard error; question 405.1 is just asking about the properties of the given distribution. To contrast, let me ask a question that does invoke the standard error (which, in this case, is the standard deviation of a sample mean not a...
    HI @theproman23 There is no sample so there is no standard error; question 405.1 is just asking about the properties of the given distribution. To contrast, let me ask a question that does invoke...
    Replies:
    14
    Views:
    381
  27. Nicole Seaman

    P1.T2.406. Distributions II

    Hi @fjc120 F-distiribution is on page 60 of P1.T2. Miler (see below). It's also in the Miller reading, although personally I do not find Miller's explanation awesomely helpful. See also ; i.e., we just take the ratio of the two sample variances, and this F-ratio (aka, variance ratio) is used to test the null hypothesis that the (underlying population) variances are equal. If the population...
    Hi @fjc120 F-distiribution is on page 60 of P1.T2. Miler (see below). It's also in the Miller reading, although personally I do not find Miller's explanation awesomely helpful. See also ; i.e., we just take the ratio of the two sample variances, and this F-ratio (aka, variance ratio) is used to test the null hypothesis that the (underlying population) variances are equal. If the population...
    Hi @fjc120 F-distiribution is on page 60 of P1.T2. Miler (see below). It's also in the Miller reading, although personally I do not find Miller's explanation awesomely helpful. See also ; i.e., we just take the ratio of the two sample variances, and this F-ratio (aka, variance ratio) is used to...
    Hi @fjc120 F-distiribution is on page 60 of P1.T2. Miler (see below). It's also in the Miller reading, although personally I do not find Miller's explanation awesomely helpful. See also ; i.e.,...
    Replies:
    21
    Views:
    243
  28. David Harper CFA FRM

    L1.T2.62 Expectation & variance of variable

    Hi @bpdulog (b) is a constant, given the domain it must be 0.10, such that the function is: f(x) = 0.1*x over [0, 1, 2, 3, 4]. So f(1) = 0.1, f(2) = 0.2, f(3) = 0.3 and f(4) = 0.4; these sum to 1.0 per the definition of a probability (the requirement is how we solved for constant b). Separately, we can ask, what is the mean of this function? The answer to that question is the sum of X*f(x),...
    Hi @bpdulog (b) is a constant, given the domain it must be 0.10, such that the function is: f(x) = 0.1*x over [0, 1, 2, 3, 4]. So f(1) = 0.1, f(2) = 0.2, f(3) = 0.3 and f(4) = 0.4; these sum to 1.0 per the definition of a probability (the requirement is how we solved for constant b). Separately, we can ask, what is the mean of this function? The answer to that question is the sum of X*f(x),...
    Hi @bpdulog (b) is a constant, given the domain it must be 0.10, such that the function is: f(x) = 0.1*x over [0, 1, 2, 3, 4]. So f(1) = 0.1, f(2) = 0.2, f(3) = 0.3 and f(4) = 0.4; these sum to 1.0 per the definition of a probability (the requirement is how we solved for constant b). Separately,...
    Hi @bpdulog (b) is a constant, given the domain it must be 0.10, such that the function is: f(x) = 0.1*x over [0, 1, 2, 3, 4]. So f(1) = 0.1, f(2) = 0.2, f(3) = 0.3 and f(4) = 0.4; these sum to...
    Replies:
    7
    Views:
    150
  29. David Harper CFA FRM

    L1.T2.86 OLS Regression

    I was barking up wrong tree as I assumed I had to include the sample size of 10 in my calculations. Thanks
    I was barking up wrong tree as I assumed I had to include the sample size of 10 in my calculations. Thanks
    I was barking up wrong tree as I assumed I had to include the sample size of 10 in my calculations. Thanks
    I was barking up wrong tree as I assumed I had to include the sample size of 10 in my calculations. Thanks
    Replies:
    6
    Views:
    98
  30. David Harper CFA FRM

    L1.T2.83 Regression function

    Please see An estimator is basically a statistic as opposed to a parameter (although if we want to get technical, here is ). As such, to my knowledge, a tell-tale sign of an estimator would be that it varies (even if slightly) with each different sample. In the case of a SRF, each time we regress based on a different draw of observations (from the same population), the slope coefficient...
    Please see An estimator is basically a statistic as opposed to a parameter (although if we want to get technical, here is ). As such, to my knowledge, a tell-tale sign of an estimator would be that it varies (even if slightly) with each different sample. In the case of a SRF, each time we regress based on a different draw of observations (from the same population), the slope coefficient...
    Please see An estimator is basically a statistic as opposed to a parameter (although if we want to get technical, here is ). As such, to my knowledge, a tell-tale sign of an estimator would be that it varies (even if slightly) with each different sample. In the case of a SRF, each time we...
    Please see An estimator is basically a statistic as opposed to a parameter (although if we want to get technical, here is ). As such, to my knowledge, a tell-tale sign of an estimator would be...
    Replies:
    3
    Views:
    76

Thread Display Options

Loading...