Question

Clear handwriting

The number of emails that I get in a weekday can be modeled by a Poisson distribution with an average of 0.2 emails per minute. What is the probability that I get no emails in an interval of length 5 minutes? What is the probability that I get more than 3 emails in an interval of length 10 minutes? 3. a) b)

Answer 1

a)

Since average rate of email is 0.2 emails per minute so the average rate of emails is 5 minute is

$\lambda=0.2\cdot 5=1$

The probability that I get no emails in an interval of length 5 minutes is

$P(X=0)=\frac{e^{-1}1^{0}}{0!}=0.36788$

b)

Since average rate of email is 0.2 emails per minute so the average rate of emails in 10 minute is

$\lambda=0.2\cdot 10=2$

The probability that I get more than 3 emails in an interval of length 10 minutes is

$P(X>3)=1-P(X\leq 3)=1-\sum_{x=0}^{3}\frac{e^{-2}2^{x}}{x!}=0.14288$