Question

The number of people who enter a drugstore in a given hour is a Poisson random variable with parameter λ = 10 . Compute the conditional probability that at most 3 men entered the drugstore, given that 10 women entered in that hour. What assumptions have you made?

Answer 1

Answer:

P( X ₙ ≤ 3) = e⁻³ [1+5+5²/2!+5²/3!]

Step-by-step explanation:

There are different way to solve it

Number of men and women entering are two separate Poisson random variable , with total number of people entering with rates being the sum of two. Poisson distributed with λ M

and for women

Poisson distributed with λ W

If we assume that men and women come in same rate then

λ M = λ W

But from the problem we see that

λ M + λ W = 10

M ≈Poisson{x;5}

P( X ₙ ≤ 3) = e⁻³ [1+5+5²/2!+5²/3!]