Question

Weibull Distribution

1) Let a be the time you have to wait until the next customer arrives at a store (in minutes). Assume the mean of a is 1.000 minute).

Determine the pdf for the time it takes for three customers to arrive (the sum of three exponential distributions)

Determine a Weibill distribution to approximate this pdf.

Answer 1

GIVEN THAT:-

According to the question we have that

"a" is the time take for the next coustemer to arrive to the store and the time is measured in minutes here ,

now here that

TO FIND :- The pdf for the time it takes for the three customers to arrive

so now we get that ,.     

S =X1+ X2+ X3

S follow gamma distribution with parameter k = 3 and theta = 1

pdf = x^(3-1) e^(-x) / 2!
= e^(-x) * x^2/2

the above is the pdf tsken for the three customers to enter the shop

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