Solve part C by R -programming coding :

Exercise 5.14 Consider a sample of size n from a mixture distribution with unknown weights, Xi ~ dg(x) + (1-0)h(x), i = 1, . . . , n, where g() and h() are known a. Introduce Z1,..., Zn, where Zi indicates the distribution from which X; has been drawn, so Show that the complete-data likelihood can be written as 72 b. Show that EZi e.ri] = 9(24)/[dg(m) + (1-0)h(m), and deduce that the EM sequence is given by ()g(zi) c. Examine the convergence properties of this EM algorithm on a simulated dataset p(0-2)/2)/2, where yo denotes with n 25, = 0.3, h(2) = y(2), and g(x) the N (0,1) density Exercise 5.14 Consider a sample of size n from a mixture distribution with unknown weights, Xi ~ dg(x) + (1-0)h(x), i = 1, . . . , n, where g() and h() are known a. Introduce Z1,..., Zn, where Zi indicates the distribution from which X; has been drawn, so Show that the complete-data likelihood can be written as 72 b. Show that EZi e.ri] = 9(24)/[dg(m) + (1-0)h(m), and deduce that the EM sequence is given by ()g(zi) c. Examine the convergence properties of this EM algorithm on a simulated dataset p(0-2)/2)/2, where yo denotes with n 25, = 0.3, h(2) = y(2), and g(x) the N (0,1) density