A die is loaded in such a way that an even number is twice likely tooccur as an odd number. If the die is tossed twice, find the probabilitydistribution of the random variable X representing the perfect squares in thetwo tosses.

A die is loaded in such a way that an even number is twice likely tooc

1.	A die is loaded in such a way that an even number is twice likely tooccur as an odd number. If the die is tossed twice, find the probabilitydistribution of the random variable X representing the perfect squares in thetwo tosses.
Answer» let the probability of odd no be `p` let the probability of even no be `2p` `p+p+p+2p+2p+2p =1` `9p = 1 ` `p = 1/9` let x= perfect square x = 4,9 `p(x)= P(x) or p(9) = p(4) + p(9)` `p(x) = p.p + 2p.2p +p.p + p.2p + 2p.p + p.2p + 2p.p` `p^2 + 4p^2 + p^2 + 8p^2 = 14p^2` `p(x) = 14p^2` `= 14* 1/9^2 = 14/81`