Observe that for a random variable Y that takes on values 0 and1, the expected value of Y is defined as follows:Upper E left p
arenthesis Upper Y right parenthesis equals 0 times Pr left parenthesis Upper Y equals 0 right parenthesis plus 1 times Pr left parenthesis Upper Y equals 1 right parenthesisE(Y) = 0×Pr(Y=0)+1×Pr(Y=1)Now, suppose that X is a Bernoulli random variable with success probability Pr (X =1)= p. Use the information above to answer the following questions.Show thatUpper E left parenthesis Upper X cubed right parenthesis equals pEX3=p.Upper E left parenthesis Upper X cubed right parenthesisEX3=(00times×1 minus p1−p)+(11times×p)= pp(Usethe tool palette on the right to insert superscripts. Enter you answer in the same format asabove.)Suppose that p =0.120.12.Compute the mean of X.Upper E left parenthesis Upper X right parenthesisE(X)= nothing(Roundyour response to two decimalplaces)
