Topic: Discrete Random Variables. [10 pts] The following two functions are 'almost' considered to be probability mass functions (pmfs) which are defined on the positive integers {1, 2, 3,...} . PX, (2) = B1 - 2-2. . PX2 (IT) = B2 - 27 / c!. (where a! = x . (x - 1) . (x - 2) . ... . 1). Here, B, and B2 are called normalizing constants. 1. [1 pt] In order for px (z) to be a valid probability mass function. We need what condition to hold? 2. [3 pts] Find B, and B2 such that px, (r) and px, (x) are valid pmfs. Hints. no a . r" = = 1", for |r| 1) and P(X2 > 1). (b) [2 pts] The most probable value of X1 and X2. (c) [2 pts] The probability that X1 is even