The probability distribution function of a random variable, X is given by f(x)=k(x2 −1) where x=2,3,4,5

Let F(x) be the c.d.f of X.

(a) The random variable X is continuous. True or false?

(b) f(x) is a probability mass function. True or false? (c) Construct the probability distribution table for X.

(d) Determine the value of the constant, k. (e) Find the E(X), SD(X), V ar(X) and modeX , medX . (f) Find the values of f(3.5) and F(3.5). (g) Sketch f(x), the probability distribution function.

(h) Sketch F(x), the cumulative distribution function of X.