(Solved): 1) X is a Bernoulli random variable with Pr(X=1)=0.99;Y is distributed N(0,1);W is distributed N(0, ...
1) X is a Bernoulli random variable with Pr(X=1)=0.99;Y is distributed N(0,1);W is distributed N(0,100); and X,Y, and W are independent. Let S=XY+(1?X)W. (That is, S=Y when X=1, and S=W when X=0.)
d. Derive E(S),E(S2),E(S3), and E(S4). (Hint: Use the law of iterated expectations conditioning on X=0 and X=1.) e. Derive the skewness and kurtosis for S.