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+3 votes
x1 x2 x3 are  three independent random variables distributed uniformly on [0,1].Find probability that P(X1 is largest )
asked in Probability by Veteran (33.2k points) | 378 views
I m getting 1/12.

1 Answer

+2 votes
probability is 1/3..

Solution:- there are 6 cases P(x1>x2>x3), P(x1>x3>x2), P(x2>x1>x3), P(x2>x3>x1), P(x3>x2>x1), P(x3>x1>x2).

All cases are equally likely and hence P(x1) being largest is P(x1>x2>x3) or P(x1>x3>x2).

Hence, P(x1 being largest)=2/6=1/3
answered by Junior (947 points)

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