For some fixed integer k the random variable X has probabili

For some fixed integer k, the random variable X has probability mass function (pmf) given by p(x) = {c(k - x)^2 for x = 0, 1, 2, ..., k - 1 0 otherwise. Find the value of c when k = 10, 30, 100, Note sigma_r = 0^k - 1 p(x) = 1. Find P(X lessthanorequalto 5) and P(3 lessthanorequalto X lessthanorequalto 8) when k = 10, 30, 100. Note P(X lessthanorequalto a) = sigma_x - 0^a p(x) and P(c lessthanorequalto X lessthanorequalto d) = P(X lessthanorequalto d) - P(X lessthanorequalto c - 1).

Solution

Value of k Value of C P(X<=5) P(3 <= X <= 8) 10 0.002597403 0.92208 0.361039 30 0.000105764 0.48176 0.3827599 100 2.96E-06 0.16888 0.158653