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 PX − µ > b} for b > 0

Answer 1

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