Question 1. [15 MARKS] Let X be a random variable with outcome space N2 = {a,b,c} and pla) = 0.1,p(b) = 0.2, and p(c) = 0.7. Let = = = f(x) = 10 if = a 5 if x=b 10/7 if x = c (a) [4 MARKS] What is E[f(x)]? (b) [3 MARKS] What is E[1/p(X)]? (Note: This is an expectation about the probability) (c) [4 MARKS] For an arbitrary pmf p, what is E[1/P(X)]? (Note: This is an expectation about the probability) (d) [4 MARKS] What is E[F(X)?) and E[F(X)]2