Given that x has a Poisson distribution with u= 1.7, what is the probability that x = 1? P(1) (Round to four decimal places as needed.)

Suppose that customers arrive at a diner at a Poisson rate of A = 3 per hour. What is the probability that exactly 6 customers arrive between 1PM and 3PM and that exactly 4 customers arrive between 4PM and 5PM? Hint: You're dealing with two discrete rv's, in this case. (Answer as a decimal number, and round to 3 decimal places).

Given that x has a Poisson distribution with µ = 2, what is the probability that x = 4? %3D P(4) = (Round to four decimal places as needed.)

The number of customers arriving per hour at a certain automobile service facility is assumed to follow a Poisson distribution with mean λ = 7. ​(a) Compute the probability that more than 12 customers will arrive in a 2-hour period. ​(b) What is the mean number of arrivals during a 2-hour period.