Q28 of 108 Page 271

A die is thrown three times. Let X be ‘the number of twos seen’. Find the expectation of X.

Given that, X= no. of twos seen


So, on throwing a die three times, we will have X=0,1,2,3



P(X=1) = Pnot 2. Pnot 2. P2 + P 2. P2. Pnot 2 + P 2. Pnot 2. P 2





P(X=2) =Pnot 2. P2. P2 + Pnot 2. P2. P2 + P2. Pnot 2.P2








We know that,





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For the following probability distribution determine standard deviation of the random variable X.

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A biased die is such that P (4) = 1/10 and other scores being equally likely. The die is tossed twice. If X is the ‘number of fours seen’, find the variance of the random variable X.

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Two biased dice are thrown together. For the first die P (6) = 1/2. the other scores being equally likely while for the second die, P (1) = 2/5 and the other scores are equally likely. Find the probability distribution of ‘the number of ones seen’.

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Two probability distributions of the discrete random variable X and Y are given below.



Prove that E(Y)2=2E(X).