Question
Let X1 and X2 be two independent exponentially distributed random variables with means 0.5 and 0.25, respectively. Then Y = min (X1, X2) is
Options :
exponentially distributed with mean 1⁄6
exponentially distributed with mean 2
normally distributed with mean 3⁄4
normally distributed with mean 1⁄6
Answer :
exponentially distributed with mean 1⁄6
Solution :
Mean (x1) = 0.5
1/λ1 =0.5
λ1 =1/ 0.5 = 2
Mean (x2) = 0.25
1/λ2 = 0.25
λ2 = 1/0.25 = 4
y = mean (x1, x2)
Mean(y) = 1/(λ1+λ2) = 1/(2+4) = 1/6
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