Q23 of 29 Page 1

Two numbers are selected at random (without replacement) from the first five positive integers. Let X denote the larger of the two numbers obtained. Find the mean and variance of X.

X can take values as 2,3,4,5 such that P(X – 2) = probability that the larger of two number 2 = probability of getting 1 in first selection and 2 in second selection getting 2 in first selection and 1 in second selection.

∴P(X – 2) =


Similarly,


∴P(X – 3) =


∴P(X – 4) =


∴P(X – 5) =



E(X) = 2
E() = 4


Therefore, V(X) = E(X) – E()


= 17 – 16


= 1.


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