Question

Let X denote a random variable that follows a binomial distribution with parameters n=5, p=0.3, and Y denote a random variable that has a Poisson distribution with parameter λ = 6. Additionally, assume that X and Y are independent random variables.

Derive the joint probability distribution function for X and Y. Make sure to explain your steps.

Answer 1

poisson probability distribution

P(Y=y) = e-λλy/y!

where y =0,1,2,3 -------------

Binomial probability is given by

P(X=x) = C(n,x)*px*(1-p)(n-x)

where X = 0,1,2,3,4,5

since, X and Y are independent, joint probability distribution function will be

so, P(X=x,Y=y) = P(X=x) * P(Y=y)

P(X=x,Y=y) =Σ5C x * 0.3^ x * (1-0.3)^(5-x) * e-66y/y! where, x=0,1,2,3,4,5 and y =0,1,2,3,4...................

please revert for doubts and
please UPVOTE the solution