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Let X and Y be two exponentially distributed and independent random variables with mean α and β, respectively. If Z= min (X, Y), then the mean of Z is given by
  • a)
    (1/(α + β))
  • b)
    min (α, β)
  • c)
    (αβ/(α + β))
  • d)
    α + β
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Let X and Y be two exponentially distributed and independent random va...

X and Y are two independent exponentially distributed random variables. Let λ1 and λ2 parameters of X and Y respectively.

Given, Z = min (X, Y)

Since mean of exponential distribution = 1/Parameter
So,

∴ Z is random variable with parameter
Mean of Z = 
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