The lifetime of two light bulbs are modeled as independent and exponential random variables X and Y, with parameters lambda and mu, respectively. The time at which one of those two light bulb first burns out is Z = min (X, Y), what is the PDF of Z?
1 answer:
Answer:
Step-by-step explanation:
The PDF of X is
The PDF of Y is
The means of X and Y are respectively,
so we can see that the larger the parameter, the smaller the mean. Hence the PDF of Z = min(X, Y) is an exponential with the largest parameter of the two.
Therefore, the PDF of Z is
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