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

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