Exercise 1. (PMF and CDF) (30pt). (a) Suppose the probability mass function (pmf) of Y is given by Py (0) = 5, PY (1) = =, PY(2) = OOI NO (1) Find the cumulative distribution function (cdf) of Y. (b) Find the mean value of Y (c) Suppose the probability mass function (pmf) of X is given by Px(-2) = 3, Px (0) = , 1, Px (2 ) = (2) Find the cdf of X. (d) Draw the cdf of X. (e) Find the mean value of X. (f) Suppose the probability mass function (pmf) of W is given by Pw(-1) = 2, Pw(0) = 3' , Pw (2) = =. (3) Check wether this is a valid pmf. Justify your answer of why or why not