The number of emails that I get in a weekday (Monday through Friday) can be modeled by a Poisson distribution with an average of 1/6 emails per minute. The number of emails that I receive on weekends (Saturday and Sunday) can be modeled by a Poisson distribution with an average of 1/30 emails per minute.

What is the probability that I get no emails in an interval of length 4 hours on a Sunday?

A random day is chosen (all days of the week are equally likely to be selected), and a random interval of length one hour is selected on the chosen day. It is observed that I did not receive any emails in that interval.

What is the probability that the chosen day is a weekday?

1) 0.0003355

2) 0.000838

Step-by-step explanation:

The number of emails received on Sunday can be modeled by a Poisson distribution with an average of 1/30 emails per minute.

Also; taking the probability that no email in an interval of the length of 4 hours on Sunday; we have:

Time (T) = 4 hours

= 4 × 60 minutes

= 240 minutes

Poisson Distribution can be expressed as:

8

The Poisson Probability can now be calculated by using the formula;

= 0.0003355

2)

A  random day is chosen (all days of the week are equally likely to be selected), and a random interval of length one hour is selected on the chosen day. It is observed that I did not receive any emails in that interval.

What is the probability that the chosen day is a weekday?

Let use U to represent the event that weekday(Monday - Friday) is chosen.

Hence, P(U) =

Let V represent the event that weekend( Saturday or Sunday ) is chosen.

P(V) =

Let W represent the event that no emails were received.

The probability that no emails were received during the weekday can then be illustrated as:

P ( W║U)

The Poisson Distribution for weekday (Monday - Friday ) is given by:

Probability P ( W║U) for Poisson Probability can now be determined as:

Probability that no emails we received during the weekend (Saturday or Sunday) can be illustrated as: P ( W║V).

The Poisson distribution for weekend  (Saturday or Sunday) is given by:

P ( W║V) for Poisson Probability can be be calculated as:

FInally, the probability that the chosen day is a weekday given that no emails were received in the interval of the length one hour can now be determined as:

0.000838

step-by-step explanation:

1

-1

step-by-step explanation: