Suppose X and Y are independent random Variables with the same distr.pdf
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Suppose X and Y are independent random Variables with the same distribution function F(x). Let Z = max(X, Y). What is the distribution function of Z? Solution P(Z <= z) = P(max(x,y) <= z) = P(x and y <= z) =(as x and y are independent) P(x <=z) * P(y <= z) = F(z)*F(z) = F2(z).
Suppose X and Y are independent random Variables with the same distr.pdf
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Suppose X and Y are independent random Variables with the same distribution function F(x). Let Z = max(X, Y). What is the distribution function of Z? Solution P(Z <= z) = P(max(x,y) <= z) = P(x and y <= z) =(as x and y are independent) P(x <=z) * P(y <= z) = F(z)*F(z) = F2(z).
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Suppose X and Y are independent random Variables with the same distr.pdf
- 1. Suppose X and Y are independent random Variables with the same distribution function F(x). Let Z = max(X, Y). What is the distribution function of Z? Solution P(Z <= z) = P(max(x,y) <= z) = P(x and y <= z) =(as x and y are independent) P(x <=z) * P(y <= z) = F(z)*F(z) = F2(z)