Suppose that PX 2 070PX 19 020 PX 30 010 and also that

Suppose that P(X = 2) = 0.70,P(X = 19) = 0.20, P(X = 30) = 0.10, and also that Y = |X - 14|. (a) Give the PMF of Y. (b) Using (a), give EY. (c) Using (a) and (b), give varY.

A discrete random variable X has a symmetric distribution if its nonzero possible values occur in pairs: x and -x. That is, if x <>(not equal to) 0 is a possible value, then so is -x. Further, it is also the case that p(-x) = p(x). Show the following: if X is a symmetric random variable, then for any positive value b,

P(X >=b) = P(X =< -b).

Solution

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