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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
  • a)
    exponentially distributed with mean 1⁄6
  • b)
    exponentially distributed with mean 2
  • c)
    normally distributed with mean 3⁄4
  • d)
    normally distributed with mean 1⁄6
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Let X1and X2be two independent exponentially distributed random variab...
x1 & x2: two independent exponentially distributed random variables with means 0.5 and 0.25.
A continuous random variable x is said to have an exponential (λ) distribution if it has probability density function.
Where, λ > 0, is called the rate of distribution. The mean of the exponential (λ) distribution is calculated using integration by parts as:
Let x1, x2 …..., xn be independent random variables, with xi having exponential (λi) distribution. Then the distribution of min (x1, x2 ……, xn) is exponential (λ1 + λ2 + …. + λn)
Thus, y = min (x1, x2) is exponentially distributed with mean (1/6).
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Let X1and X2be two independent exponentially distributed random variables with means 0.5 and 0.25, respectively. Then Y = min (X1, X2) isa)exponentially distributed with mean 1⁄6b)exponentially distributed with mean 2c)normally distributed with mean 3⁄4d)normally distributed with mean 1⁄6Correct answer is option 'A'. Can you explain this answer?
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