Question

Messages arrive at a computer at an average rate of 25 messages per second. The number of messages that arrive in 1 second is known to be a Poisson random variable. a. Find the probability that no message arrive in 1 second. b. Find the probability that more than 5 messages arrive in a 10-second period.

Answer 1

Answer:

a)$1.3887943865 \times 10^{-11}$

b)P(X>5)=1

Step-by-step explanation:

$P(X=x)=\frac{e^{-\lambda} \lambda^k}{k!}$

We are given that Messages arrive at a computer at an average rate of 25 messages per second.

$\lambda = 25$

a) Find the probability that no message arrive in 1 second.

$P(X=0)=\frac{e^{-25} (25)^0}{0!}\\P(X=0)=\frac{e^{-25} (25)^0}{0!}\\P(X=0)=1.3887943865 \times 10^{-11}$

b) Find the probability that more than 5 messages arrive in a 10-second period.

$P(X>5)=1-P(X \leq 5)$

$P(X>5)=1-\sum_{0}^{10} (P(X=0)+P(X=1)+........+P(X=5))$

P(X>5)=1