Question is in the attachment.

1. Consider a random variable x with the probability distribution filth} = cx + B][r+1] where r and B are some suitable positive real para meters, and x a It]. {a} From the normalization condition, determine c such that fit is a proper probability distribution {b} Calculate the mean and variance. lc] Now we men; need to take care whether restrictions are to be made on the para meters r and B: no mean and variance assume nite values for all positive values of r and all positive values of B? Justify? 1pour answers. {d} } Calculate the numerical value of mean and variance {when these are finite, check!) for r := F and B = 2 + DAB'CDEF where ABCDEF are the digits of 1your Iiidigit candidate number