The probability function of a discrete random variable X is given by

for some integer n ≥ 2 and a suitable constant c.
(i) Prove that c = 2.
(ii) Find the expected value E(X) and the variance Var(X).

(iii) Assuming that n ≥ 5, calculate the probabilities

Transcribed Image Text:

c(n-x) f(x)= x=1,2,...,n-1, n(n - 1)'