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The length of a google search by an individual is exponentially distributed with parameter lamda. Find...

The length of a google search by an individual is exponentially distributed with parameter lamda. Find the joint distribution of length of time for 100 unrelated individuals. Simplify as much as possible your final expression, using summation or product operators or powers or n, as needed.

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Answer #1

Let indicate the length of a google search by ith individual, where i=1,2,...,100. We can assume that the length of a google search by one individual is independent of another as these are unrelated individuals and each of these have the same distribution, i,e. each of them are exponentially distributed with parameter .

That means the length of a google search by these 100 individuals are random numbers indicated by . These are iid (independent and identically distributed) exponential with parameter

The pdf of is

Since these are independent, the joint probability is just the product of individual pdfs.

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