Question: Let $X_{1), X_{2), X_{3}$ be independent, identically distributed continuous random variables. Find the probability that the second largest value (i.e., the median) is closer to

$Let $X_{1), X_{2), X_{3}$ be independent, identically distributed continuous random variables.$

Let $X_{1), X_{2), X_{3}$ be independent, identically distributed continuous random variables. Find the probability that the second largest value (i.e., the median) is closer to the smallest value than to the largest value, when the common distribution of the $X_{i}$ is (a) the Uniform $(0,1)$ distribution (a symmetry argument should suffice here); (b) the Exponential $(\lambda)$ distribution. S.P.PB. 327

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