# Statistics: Joint Probability Distribution Problem

• Oct 21st 2008, 11:05 PM
ashinynicklel
Statistics: Joint Probability Distribution Problem
The following table gives the joint probability function of return on stocks (X) and returns on bonds (Y).

http://img56.imageshack.us/img56/2149/aaastatak1.jpg

What is the expected value of return on stocks? This is (.3)(-10)+(.7)(10)=4
What is the expected value of return on bonds? This is (.4)(0)+(.6)(5)=3
What is the variance of returns on stocks?
What is the variance of returns on bonds?
What is the covariance of returns on stocks and bonds?

I'm not exactly sure how to proceed with calculating variance. I think I'm just misapplying the formula for this seemingly easy problem but my answers just aren't matching up. Can someone help?
• Oct 22nd 2008, 12:05 AM
mr fantastic
Quote:

Originally Posted by ashinynicklel
The following table gives the joint probability function of return on stocks (X) and returns on bonds (Y).

http://img56.imageshack.us/img56/2149/aaastatak1.jpg

What is the expected value of return on stocks? This is (.3)(-10)+(.7)(10)=4
What is the expected value of return on bonds? This is (.4)(0)+(.6)(5)=3
What is the variance of returns on stocks?
What is the variance of returns on bonds?
What is the covariance of returns on stocks and bonds?

I'm not exactly sure how to proceed with calculating variance. I think I'm just misapplying the formula for this seemingly easy problem but my answers just aren't matching up. Can someone help?

\$\displaystyle Var(X) = E(X^2) - [E(X)]^2\$

Let X be the random variable value of return on stocks.

\$\displaystyle E(X) = 4\$, as you already know. \$\displaystyle E(X^2) = (0.3)(-10)^2 + (0.7)(10)^2 = 30 + 70 = 100\$.

Therefore \$\displaystyle Var(X) = 100 - 4^2 = 84\$.
• Oct 22nd 2008, 12:20 AM
ashinynicklel
Okay thank you I found the formula but wasn't sure how to apply it.

So this is the formula for covariance:

This isn't clear to me but again, how do I apply the formula for covariance? Namely what is E(X*Y)?

Sorry, I'm not really familiar with using expected values to calculate variance/covariance.
• Oct 22nd 2008, 01:28 AM
ashinynicklel
edit: got it. thanks again.