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Answer to Question #10849 in Statistics and Probability for srijita

Question #10849
suppose X and Y are independent random variables that follow the uniform distribution on the interval [0,1]. Let Z=min{X,Y}. P(Z<0.5)=?
Expert's answer
Due to X, Y are independent, one can write P(Z > 0.5) = P(X, Y >
0.5) = P(X > 0.5)P(Y > 0.5) = 0.5 ยท 0.5 = 0.25

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