The discrete random variables X and Y are independent from one another and are defined as X ~ B 16 , 0 . 25 and Y ~ P 2 . Then the sum of the variances of X and Y is

Step-by-step solution

Given, The discrete random variables X and Y are independent from one another and are defined as X ~ B 16 , 0 . 25 and Y ~ P 2 , Now given for X , n = 16 and p = 0 . 25 ,   so   q = 1 - 0 . 25 = 0 . 75 , Now variance is given by n p q = 16 × 0 . 25 × 0 . 75 = 3 And variance of Y is given as 2 , So sum of variance of X   &   Y is given by 3 + 2 = 5