Question

In: Statistics and Probability

A barber shop has an average of 12 customers between 8.00am and 9.00am every Saturday. Customers arrive according to Poisson distribution. Let X represent the time between arrivals.

(a) Construct the distribution for the random variable X?

(b) Find the mean and standard deviation of X.

Solutions

Expert Solution

Let Y be the number of customers arrived between 8:00 am to 9:00 am
Here Y~Poisson(12)

Here, X represent the time between arrivals.




.....................(i)
Now,

a) The Distribution of X is:

b) Mean and Standard Deviation:



   [as,]

Now, we are to calculate:






Standard Deviation: S.D.(X)

Mean=

S.D.=0.1443

c)Here we're asked to calculate:

[from equation (i)]

orchestra answered 1 year ago

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