The number of defects per plate of sheet metal is a Poisson random variable N with a parameter λ = 10. The inspection process has a constant probability of 0.9 of finding each defect, and the successes are independent, that is, if M represent the number of defects found, then for a given N = n (the number of defects per plate), we have: P(M= m|N= n)= (n)0.9ᵐ x 0.1ⁿ⁻ᵐ, m≤n
Find the joint probability mass function of M ad N.