(i) Recall that X can be expressed as X = _ _, Bi, where B1, ..., Bn are independent Bernoulli rvs. Use this fact to show that the MGF of a binomial random variable X with parameters (n, 0) is Mx(t) = (0et + 1 - 0)". (1) (Hint: For independent random variables Effi( B1) f2(B2) x. . .xfk(BK)] = [It_, Elfk(Bk)].) (ii) Use the MGF to show EX] = no (2) E[X2] = n(n - 1)02 + no. (3) (iii) We saw in class how to estimate 0 using (2). Can we instead use (3) and the analog principle to estimate 0? Explain. (iv) As we saw in Classs 7, ExampleBinom. cav contains data on the number of cars that stopped at an intersection. Using the method you explained in (iii), report your estimate of 0. Compare it to the estimate of 0 based on (2). Summarize your findings. (v) Set 0 to the value you obtained in (iv). Compare the PMF to the histogram obtained from the data. Summarize your findings