# Query 1 - Probability Distribution

Discussion in 'P1.T2. Quantitative Methods (20%)' started by Avishek, Sep 30, 2007.

1. ### AvishekNew Member

Thanks David for the previous explanation on the Log query.

I will be posting all my queries now on as and when I come across. Am sure it will help many of your members too.

Ques: Use the following probability distribution to calculate the standard deviation for the portfolio.

State of the Economy:

Boom ->
Probability: 0.30
Return on Portfolio: 15%

Bust ->
Probability: 0.70
Return on Portfolio: 3%

A) 6.0%.

B) 5.5%.

C) 6.5%.

D) 7.0%.

Regards, Avishek

2. ### David Harper CFA FRMDavid Harper CFA FRM (test)Staff Member

Avishek,

What is the source of this question?

Do you see that the quiz has explanations - hit 'i' or click on the magnifying glass, and the answer is explained?

David

3. ### AvishekNew Member

David,

This was a question shot by someone in my Googlegroup community... I tried to solve it...

The place where am getting stuck up is on the calc of the mean... The actual calculation of the mean was deriving an answer of .667 or .0667... But I was not able to trace how.

Can you throw some light on the mean calculation?

Aprpeciate it.

Also is this forum not meant for external queries? I feel we can all try and make it more interactive by shooting any kind of queries provided they stick to the curriculum.

Looking forward to hear from you positively.

Avishek

4. ### David Harper CFA FRMDavid Harper CFA FRM (test)Staff Member

Avishek,

Var(x) = Covariance (x,x) = E(XX) - E(X)E(X) = E(X^2) - E(X)^2

E(X) = Average(X) = (70%)(3%)+(30%)(15%) = 6.6%
E(X^2) = Average (X^2) = (70%)(3%^2)+(30%)(15%^2) = about 0.74%

E(X^2) - E(X) = 0.74% - 6.6%^2 = about .302%. That's variance, so SQRT(0.302%) = 5.5%

Yes, I very much agree with you, the forum is a fine place for external questions *if* they are relevant to the upcoming exam (this question is!)...It helps to know the source: I have seen plenty of ad hoc questions that are interesting or relevant to old exams but would distract current candidates, so knowing the context is good. (Also, you'll notice there is a question somewhere on this forum about external definitions on tracking error and relative VaR, where the outside source is credible, but the definitions are different than FRM 2007, so I *agree* with you, if it helps for the exam, I welcome it!)

Thanks,
David