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Let X1 and X2 be independent random variables with distribution funct.pdf

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This document describes two independent random variables X1 and X2 with distribution functions F1 and F2. It asks to show that the distribution function Fmin of the random variable defined as the minimum of X1 and X2, min(X1,X2), is equal to 1-(1-F1)(1-F2).

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Let X1 and X2 be independent random variables with distribution functions F1 and F2, respectively. Let Fmin be the distribution function of the random variable min(X1,X2). Show that Fmin=1(1F1)(1F2).

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  • 1. Let X1 and X2 be independent random variables with distribution functions F1 and F2, respectively. Let Fmin be the distribution function of the random variable min(X1,X2). Show that Fmin=1(1F1)(1F2).