Suppose that X, Y, and Z are independent, with E[X]=E[Y]=E[Z]=2, and E[X2]=E[Y2]=E[Z2]=5.
Find cov(XY,XZ).
(Enter a numerical answer.)
cov(XY,XZ)=
Let X be a standard normal random variable. Another random variable is determined as follows. We flip a fair coin (independent from X). In case of Heads, we let Y=X. In case of Tails, we let Y=−X.
Is Y normal? Justify your answer.
yes
no
not enough information to determine
Compute Cov(X,Y).
Cov(X,Y)=
Are X and Y independent?
yes
no
not enough information to determine
Problem 3. Problem 1(c)
Find P(X+Y≤0).
P(X+Y≤0)=
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