Q30 of 108 Page 271

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



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


Since, we have to prove that, E(Y2) =2E(X) -----(i)


Taking LHS of equation (i), we have:


E(Y)2= Y2P(Y)



=


……(ii)


Now taking RHS of equation (i) we get:


E(X)= XP(X)




……..(iii)


Thus, from equations (ii) and (iii), we get:


E(Y2) =2E(X)


Hence proved.


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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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