Let X1, X2, ..., Xn be independent random variables with PDF f(x) and CDF F(x).a.) Find the PDF of the random variable Y1=max(X1,X2,...,Xn). (Hint: The answer is nF(x)(n−1)f(x))b.) Find the PDF of the random variable Y2=min(X1,X2,...,Xn).c.) If possible, find the PDF of the random variable Y3=med(X1,X2,...,Xn). (med = median)Now, let X1, X2, ..., Xn be independent exponential random variables with rate parameters λ1,λ2,...,λn, respectively.d.) Find the PDF of the random variable Y4 = min(X1, X2, ..., Xn) (Hint: The correct answer is min(X1, X2, ..., Xn) ? Exp(λ1,λ2,...,λn).e.) Find the PDF of the random variable Y5=max(X1,X2,...,Xn)f.) If possible, find the PDF of the random variable Y6=med(X1,X2,...,Xn)