The number of emails that get in a weekday monday through...

The number of emails that get in a weekday (Monday through Friday) can be modeled by a Poisson distribution with an average of & emails per minute. The number of emails that receive on weekends Saturday and Sunday) can be modeled by a Poisson distribution with an average of 30 emails per minule_ What is the probability that get no emails in an interval of length 4 hours on a Sunday? (b) 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 did not receive any emails in that interval_ What is the probability that the chosen day is a weckday?

Transcript

0:00 Hello students.

00:01 Here we have the number of emails that gets in a weekday is modeled by a poison distribution, with an average of 1 divided by 6 males per minute.

00:17 Okay and on sunday and saturday, the average is 30 emails per minute.

00:24 In part of the day we have to find out the probability that no male may have to be a lot of the average.

00:30 Email in an interval of length four hours on sunday probability that get no emails in interval of length four hours on a sunday and in part b we have to find a random day's chosen and there is no emails in that interval so we have to find the probability that the chosen day is a week day okay so let me start with part in part in as we know for sunday and saturday the average is one divided by 30 one divided by 30 emails per minute okay so here we have to consider four hours four hours and that's equal to four multiplied by 60 minute so that's equal to 200 and four 40 minutes.

01:34 340 minutes.

01:39 So this is 1 .2 by 30 emails per minute.

01:46 Okay.

01:49 So now we can find the poison parameter.

01:54 Since it uses poison distribution, you can add the poison parameter, which is denoted as lambda.

02:08 Okay.

02:09 The poison parameter is, divided by lambda is equal to 240 minutes multiplied by 1 divided by 30.

02:21 And that's equal to 8.

02:27 Okay? now, so this is the equation for the poison distribution.

02:34 P.

02:34 Of x equal d -res minus lambda, lambda restricts, divided by h factory.

02:38 So here we have to find the probability that no emails, no.