Suppose (X) is a Bernoulli random variable with (operatorname{Pr}(X=1)=p). a. Show (Eleft(X^{3} ight)=p). b. Show (Eleft(X^{k} ight)=p)

Suppose \(X\) is a Bernoulli random variable with \(\operatorname{Pr}(X=1)=p\).

a. Show \(E\left(X^{3}\right)=p\).

b. Show \(E\left(X^{k}\right)=p\) for \(k>0\).

c. Suppose that \(p=0.3\). Compute the mean, variance, skewness, and kurtosis of \(X\).