Question

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...

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.

  1. Is Y normal? Justify your answer.

    yes

    no

    not enough information to determine

  2. 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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