Question: X is a Bernoulli random variable with Pr(X = 1) = 0.99, Y is distributed N(0. 1), and W is distributed N(0. 100). Let S

X is a Bernoulli random variable with Pr(X = 1) = 0.99, Y is distributed N(0. 1), and W is distributed N(0. 100). Let S XY+(1-X)W. (That is. SY when X 1, and SW when X = 0.)

a. Show that E(Y2) = 1 and E(W2) = 100.

b. Show that E(Y) = 0 and E(W) = 0. (Hint: What is the skewness for a fummatrio dictribution?)

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