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2.2 Random Variables > 2.2 Random Variables - Pg. 17

2.2. R A N D O M V A R I A B L E S 17 For a r a n d o m variable X , we use X - x to d e n o t e t h e subset containing all elements e r ft t h a t X m a p s to the value of x. T h a t is, X - x represents the event {e such t h a t X ( e ) = x}. N o t e the difference b e t w e e n X a n d x. Small x denotes any element in t h e space of X , while X is a function. Example 2 . 1 0 Let f~, P, and X be as in Example 2.9. Then X-3 represents the event { (1, 2), (2, 1) } and 1 P(X- Notice t h a t 3) - 18" Z xEspace(X) Example P(X - x) -- 1. 2 . 1 1 Let f~, P, and Y be as in Example 2.9. Then P ( Y - o d d ) + P ( Y - even)