GATE ME 2018 Set 2 — Question 37
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Question
Let and be two independent exponentially distributed random variables with means 0.5 and 0.25, respectively. Then is
Correct answer
(A) exponentially distributed with mean 1/6
Solution
For independent exponentially distributed random variables and with rates and , the random variable is also exponentially distributed with rate .
Given:
The mean of is .
Thus, is exponentially distributed with mean 1/6.
Given:
- Mean of
- Mean of
The mean of is .
Thus, is exponentially distributed with mean 1/6.
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