# Random variables

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)

Ray Vickson
Homework Helper
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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)

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.

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

I like Serena
Homework Helper
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##...

Ray Vickson