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# P1.T2.300.1 Probability functions Question

#### PortoMarco79

##### New Member
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Hi

It has been 15 years since I last touched this stuff. I am very much not up to snuff any more.

Can someone assist?

How does: f(x) = x/8 - 0.75

become: F(X) = x^2/16 - 0.75*x + c.

Thanks

#### brian.field

##### Well-Known Member
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f(x) is a probability density function. The integral of pdf from -infinity to +infinity must equal 1.

Capital F represents the Cumulative Density Function of CDF which is also represented by the integral of the pdf from -infinity to a and is interpreted as the probability that X <= a.

As a convention, f(x) represents the pdf and the corresponding capital letter, F(x) in this case, represents the CDF.

#### ShaktiRathore

##### Well-Known Member
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Hi,
Its the simple integration of the f(x) , probability density function which should yield Cumulative Density Function F(x),
F(x)=CDF= integration of f(x)= x/8 - 0.75
F(x) = integration of[(x/8)dx - 0.75 dx]
F(x) = integration of[(xdx/8) - 0.75 dx]
F(x) = ((x^2/2)/8) - 0.75x +c sin ce the integration of x is x^2/2.
F(x) = (x^2/16) - 0.75x +c
THanks

#### ravinaghotra

##### New Member
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Hello, can you please help and let me if we can use calculator so solve the above. I am using BA II Plus. What keys should be entered on the calculator.

#### brian.field

##### Well-Known Member
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This is not really a calculator type problem - you need to know how to integrate the function which is something that you need to be able to using calculus. (Although you could probably pass this exam without any calculus, in other words, I wouldn't spend time reviewing calculus instead of other FRM aims.)

#### ShaktiRathore

##### Well-Known Member
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Hi,
Yes I agree with Brian this types of problem shall not come where integration of some function is being asked only basic math shall come ,it is possible that some exceptional problem may come around so its better that you take some fresher course in calculus,as many concepts also demand understanding of basic fresher man calculus. Calculator BA II Plus has not integrate function i think.
also visit to see David views: https://www.bionicturtle.com/forum/...entiate-integrate-equations-in-the-exam.8814/
thanks

Subscriber
Isn't it 0.7?

#### desh

##### New Member
plz elaborate ? correct answer given is 0.80

#### PortoMarco79

##### New Member
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This is really not my strong point but, I figure that since you have 6 chances out of 10 to pick an industrial stock and 8 chances out of 10 to pick an industrial bond, you have 14 chances out of 20 to pick an industrial security.

14/20 = 0.7

#### PortoMarco79

##### New Member
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Ok. I misread the question. Sorry.

You are trying to pick a Bond (B) and an Industrial security (I).

P(B) = 10/20 (10 bonds in the pool 10 equities in the pool)
P (I) = 14/20 (6 utilities in the pool, 14 industrials in the pool)

So, you are trying to figure out the P (B & I) --which is the probability of picking B (10) + the probability of picking I (14) minus the probability of picking B or I (avoid double counting) (8)

10 + 14 - 8 = 16

16 / 20 = 0.8

I think this image sums it up best: #### PortoMarco79

##### New Member
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Can some of the more polished forum members please validate my statement above? I am really not confident in my probabilities!

#### ami44

##### Active Member
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Can some of the more polished forum members please validate my statement above? I am really not confident in my probabilities!
PortoMarco79,

Maybe a little easier way to come to the result is to count all the securities that are bonds or issued by industral firms, which are 16 (10 bonds + 6 stocks) and 16/20 = 0.8

Minor Nitpick, you write:
minus the probability of picking B or I
Imho this should be
"minus the probability of picking B and I"

#### PortoMarco79

##### New Member
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Minor Nitpick, you write:

Imho this should be
"minus the probability of picking B and I"
Yup. Was fully aware of it to, just slipped out in error! Hope not to repeat that error at the exam haha

#### tkvfrm

##### New Member
Hi PortoMarco, can you please put in the numbers in the image please..at least a description. I ma not able to figure out the probability of picking B&I in the venn image

#### Bansari

##### New Member
Assume a loss severity given by (x) can be characterized by a probability density function (pdf) on the domain [1, e^5]. For example, the minimum loss severity = $1 and the maximum possible loss severity = exp (5)~=$148.41. The pdf is given by f(x) = c/x as follows: f (x) = C/X s.t. 1 < x < e^5 where x =|loss severity |

What is the 95% value at risk (Var) i.e. given that losses are expected in positive values, at what loss severity value (x) is only 5 percent of the distribution greater than (x).

Please elaborate and explain the above question and provide easy solution @brian.field

#### ShaktiRathore

##### Well-Known Member
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Hi,
Let 95% value at risk (Var) be X.
integration from 1 to e^5( f(x)dx) =1=> integration from 1 to e^5 (c ln(x) )=> c(5-0)=1=>c=1/5
integration from X to e^5 (f(x)dx) = integration from X to e^5 (c/x dx) = integration from X to e^5 (c ln(x)) = (1/5)*(-ln(X)+5)=.05 =>lnX=4.75 =>X=e^4.75 = $115.58 Thus at$ 115.58 only 5 percent of the distribution greater than (x).

thanks