Emails arrive at the server of a company at the rate of 10 per hour. It is assum

Question

Emails arrive at the server of a company at the rate of 10 per hour. It is assumed that a Poisson process is a good model for the arrivals of the emails.

Part a)

What is the probability (to 2 decimal places) that the time between two consecutive emails is more than two minutes?

Part b)

Consider the total waiting time (in minutes) for three consecutive emails to arrive. Which of the following is a plot of the density function for this random variable?

Explanation / Answer

Emails arrival rate = 10 per hour

(A)
Email arrival rate = 10/60*2 = 0.6667 per 2 mins

Time between two consecutive emails is more than two minutes, this means less than 2 emails arrived in 2 mins

P(X<2) = P(X=0) + P(X=1)
P(X=0) = (0.6667)^0*e^(-0.6667)/0! = 0.5134
P(X=1) = (0.6667)^1*e^(-0.6667)/1! = 0.3423
P(X<2) = 0.5134 + 0.3423 = 0.8557

(C)
Email arrival rate = 10/60*5 = 0.8333 per 5 mins

P(X<3) = P(X=0) + P(X=1) + P(X=2)
P(X=0) = (0.8333)^0*e^(-0.8333)/0! = 0.4346
P(X=1) = (0.8333)^1*e^(-0.8333)/1! = 0.3622
P(X=2) = (0.8333)^2*e^(-0.8333)/2! = 0.1509

P(X<3) = 0.9477

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.