# Density Function (Poisson, Binomial)

(a) If X ~ Poisson ........, compute Mx(t).

(b) Show that if Xn ~ Binomial {see attachment} then Mxm(t) converges to Mx(t) for every t, where X ~ Poisson .......

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See attachment please! Hope it helps.

a) Since X~ , the density function is

By the ...

#### Solution Summary

(a) If X ~ Poisson ........, compute Mx(t).

(b) Show that if Xn ~ Binomial {see attachment} then Mxm(t) converges to Mx(t) for every t, where X ~ Poisson .......

Binomial and Poisson Probability Distributions

Suppose you, as the manager of Tennessee Grilled Pork. would like to ensure you have enough cleaning staff for your dining room and would like to analyze data for customers who enter the restaurant to place and order and either eat in the restaurant or take their order to- go. If the probability that a customer will stay in the restaurant to eat is .60, use the Binomial Probability function to determine the probability that 3 out of 4 customers entering the restaurant to place an order will eat their food in the room:

Using the Binomial Probability table, calculate the probability that at least 12 out of 18 customers entering the restaurant to order will eat their food in the dining room:

If the mean arrival rate for customers during the lunch rush is 6 every 10 minutes, use the Poisson distribution function to determine the probability that exactly 7 customers arrive in a 10 minute period.

Using the Poisson table provided. calculate the probability that no more than 7 customers will arrive in a one-half hour period during the lunch rush.

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