Question

A group of 2n people, consisting of n men and n women, are to be independently distributed among m rooms. Each woman chooses room j with probability pj while each man chooses it with probability qj,j=1,…,m. Let X denote the number of rooms that will contain exactly one man and one woman. (a) Find µ = E[X] (b) Bound P{|X − µ} > b} for b > 0

Answer 1

Step-by-step explanation:

Assume that

$X_i = \left \{ {{1, If , Ith, room, has,exactly, 1,man, and , 1,woman } \atop {0, othewise} \right.$

hence,

$x = x_1 + x_2+....+x_m$

now,

$E(x) = E(x_1+x_2+---+x_m)\\\\E(x)=E(x_1)+E(x_2)+---+E(x_m)$

attached below is the complete solution