Question

The number of messages sent to a computer bulletin board is a Poisson distributed random variable with a mean of 5 messages per hour. Round your answers to four decimal places (e.g. 98.7654).

(a) What is the probability that 5 messages are received in 1 hour?

(b) What is the probability that 10 messages are received in 1.5 hours?

(c) What is the probability that less than two messages are received in one-half hour?

Can anyone help me with this ?

Answer 1

@wio hey can u help me with this question ?

Answer 2

Sure.

Answer 3

\[
\Pr(X=k) = \frac{\lambda^ke^{-\lambda }}{k!}
\]

Answer 4

The mean is \(\lambda=5\)

Answer 5

(1) asks for \(\Pr(X = 5)\)

Answer 6

For (2) you as talking about 1.5 hours, so I believe you need to scale lambda.\[
\lambda' = 1.5\lambda = 1.5(5)=7.5
\]

Answer 7

And then use \(k=10\).

Answer 8

For (3) we have \[
\lambda ''=\frac 12 \lambda =\frac 12 (5) = 2.5
\]And you want to find probability for \(
k=0,1
\) individually and add them up

Answer 9

Thank you so much for your help! it was very clear and helpful :)