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The waiting times X and Y (in minutes) of two clients A and B who are...

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Basic Math

The waiting times X and Y (in minutes) of two clients A and Bwho are standing in line at two different check outs in thesupermarket are modeled as independent, exponential randomvariables with parameter 1.

(a) Find the cumulative distribution function of the randomvariable M :=min{X,Y} where min{x,y} is just the smaller value ofthe two numbers.

(b) Find the probability density function of M. Do you recognizethe socalled probability law or probability distribution of therandom variable M?

(c) What is the probability that both clients wait more than 2minutes?

Answer & Explanation Solved by verified expert
3.8 Ratings (713 Votes)
aFirst we need to find out the distributon of minimum of twoLetSince X and Y are exponentially    See Answer
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