Consider the following probability mass function for a discrete random variable : 0 1 2 x f(x) (a) Sketch the probability mass function f(x) and distribution function F(x) for this random variable. Find the mean and variance of a. (b) Now write down and sketch a probability mass function g(x) which is a mean-preserving spread of f(x). Also sketch the distribution function G(a) corresponding to g(x). What is the mean and variance of under the probability mass function g(x)?

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