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Three numbers are selected at random (without replacement) from first six positive integers. Let X denote the largest of the three numbers obtained. Find the probability distribution of X. Also, find the mean and variance of the distribution.

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The variance X takes values 3, 4,5 and 6

Alternative Method :

We have first six positive integers as 1,2,3,4,5,6.

But X can take values 3,4,5,6

[:. 1 and 2 cannot be selected since among 3 numbers the greatest is required]

P(X) = P(3 and other numbers which are less than 3) i.e., (1,2,3)

= 0.7875

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