This is in Statistics. Solve the problem below.

Solve each of the following problems. Show your complete solution neatly and legibly. If you use google sheet, submit the google sheet file. If you used R programming, submit the code and the output. Make a summary of your work. 1. (20 points) Given a random variable X with the following probability distribution: X 0 1 2 3 f(x) 5 12 12 w 32 32 32 32 Find: (a) E(X), ( b) E( X ) (c) My (1) (d) Show that M= a MX (1) = E(X) 1=0 Notes: E[g(x ] = Zg(x) f(x) for discrete random variable E[8( ] = g(x)f(x) dx for continuous random variable