Let X and Y be discrete random variables with joint probability mass function pX,Y(m, n) = fraclambda^n e^-lambda2^n m! (n - m)!, ; m = 0, dots, n, and n = 0, 1, 2, dots, where lambda is a fixed positive real number. Then which one of the following options is correct?

(C) The conditional distribution of X given Y = 3 is Bin(3, 1/2)

Q41Section ST (Statistics (Q11–Q65))41 of 65

Poisson-binomial mixture identification

Let $X$ and $Y$ be discrete random variables with joint probability mass function $p_{X,Y}(m, n) = \frac{\lambda^{n} e^{-\lambda}}{2^{n} m! (n - m)!}, \; m = 0, \dots, n, \text{ and } n = 0, 1, 2, \dots$ , where $\lambda$ is a fixed positive real number. Then which one of the following options is correct?

Pick an option to check your answer. In a mock test a wrong answer here costs 2/3 mark.

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