# Random variables

1. May 21, 2013

### ParisSpart

the random variables X1,X2... are independent and they take 0 and 1 values and they have expected value 0
if we have Y=X1+X2+...+Xn and Z=X1+X2+....+Xn+Xn+1 what is the ρ(Y,Z) for n=46

i know that ρ(Y,Z)=cov(Y,Z)/(sqrt(var(Y)*sqrt(var(Z)) but i need some help on how to find the cov and vars cov(Y,Z)=E(YZ)-E(Y)E(Z)

2. May 21, 2013

### Ray Vickson

If a random variable takes values 0 and 1 and has expected value = 0, it is zero identically----that is, it is not "random" at all! There must be an error in your problem statement.

3. May 21, 2013

### ParisSpart

sorry my mistake they take 1 and -1 values and they have expected value 0

4. May 21, 2013

### I like Serena

Hi ParisSpart!

Since there are 2 possibilities for any $X_i$ with apparent probabilities fifty-fifty... what is $\sigma^2(X_i)$?

Do you know how variances combine for independent variables?
If so, what is $\sigma^2(Y)$?

Following up, do you know how to find $\sigma^2(Z)$?

When we have all that we'll tackle $EYZ$...

5. May 22, 2013

### ParisSpart

6. May 22, 2013

### Ray Vickson

You are supposed to do you OWN work, not get somebody else to do it for you. If you cannot do the question, just accept the reduced course marks!

Last edited: May 22, 2013