After getting through security, the time (in minutes) a...

After getting through security, the time (in minutes) a person waits until boarding a flight at an airport follows an Exponential distribution with mean 45 minutes. Suppose there are 10 passengers arriving at Eppley Airport. a) What is the expected total waiting time of these 10 passengers? b) What distribution does the total waiting time follow? c) What is the standard deviation of the total waiting time?

Transcript

00:01 Hello students we are going to write here exponential distribution is given with mean value is given.

00:06 Suppose there are 10 passengers arriving at appley airport.

00:11 So in the first case what is expected total waiting time and what is the distribution does the total waiting time follow and what is the standard deviation? so if i write here for this, so let's start with our answering part.

00:26 So here, mean value is given here.

00:31 As 45 minutes so we are going to write here therefore the time a person waits could be modeled as so t s time could be modeled as exponentially distributed with one by mean this is so as a parameter for so this is a parameter as parameter as parameter for exponential distribution exponential we are going to write here for this distribution if i write here exponential distribution is equal to is equal to so let's raise this to make it more clear equal to we are going to write here for this the reciprocal of its mean the reciprocal of its mean so if i write here for this in the first case what is expected total waiting time of these 10 passengers so total expected waiting time we are going to write here for this waiting time of 10 passengers we are going to write here for this this value must be 10 multiplied by expectation of t time we are assuming here this is 10 multiplied by so expected value is 45 which is 450 minutes so in the first case answer is 4 .50 minutes as total expected time.

02:47 So this is our answer in the first case.

02:50 So now let us talk about what distribution does the total waiting time follow? the sum of the sum of identical and independent and independent exponential distribution, independent exponential distribution if i write here for this...

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