1. ## Poisson distribution HELP!!!!

I need serious help with this problem. It sounds so simple, but I can't find any way to do this.

Problem: Suppose that telephone calls enter the university's switchboard, on the average, 2 every 5 minutes. Assuming that arriving calls has a Poisson pmf with parameter 4, what is the probability of less than 7 calls in a 10 minute period.

EDIT: From what I gather, the probability of finding less than 7 would be: P(x < 7) = P(0;4) + P(1;4) + P(2;4) + P(3;4) + P(4;4) + P(5;4) + P(6;4) ???

2. Originally Posted by isuckatprobability
I need serious help with this problem. It sounds so simple, but I can't find any way to do this.

Problem: Suppose that telephone calls enter the university's switchboard, on the average, 2 every 5 minutes. Assuming that arriving calls has a Poisson pmf with parameter 4, what is the probability of less than 7 calls in a 10 minute period.

EDIT: From what I gather, the probability of finding less than 7 would be: P(x < 7) = P(0;4) + P(1;4) + P(2;4) + P(3;4) + P(4;4) + P(5;4) + P(6;4) ???
Correct.

Note: The parameter is the average of the random variable. Since the average number of calls in a 5 minute period is 2, in a 10 minute period the average number of calls is (2)(2) = 4.

3. thank you for confirming my thoughts. I thought the approach was correct but wasn't totally sure