Thread: Sigma (standard deviation) properties homework question - assistance requested

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Is there any way of doing this problem without using any identities involving covariance? (I don't know what that is).

What is the answer this problem anyway?

Possible answers: 25/4, 5/2, 9/2, 3/sqrt(2), 1/2

Let W=X+Y

P(W=-2)=.5=P(W=3)

So E(W)=.5 E(W^2)=13/2

the variance of W is 6.5-.25
now take the square root.....5/2

No need to obtain the joint distribution of X and Y, just find the distribution of W.