Question 5: Denote byD {1,2, 3, 4, 5, 6} the random variable representing a six-sided fair dice. Throw this dice and denote the outcome byd. Then, consider a. second random variableU distributed uniformly at random from the interval [0,d], where d is the value of the dice you previously threw. Answer the questions below. 5.3.) Compute the conditional expectation,E [U ID = d]. 5b) Compute the conditional variance,Var(U ID = d). 5.c) Compute the marginal probability,P(U [0, 1]). Please, input your answer as an irreducible fraction p/q, where p and q are integers. Hint: you might want to use the total probability theorem, which can be stated as follows: Given a continuous random variableX E R, a discrete random variableY E 32, and a set A C R, we have thatP(X E A) = 23,63, P(X E AlY = y)P(Y = y)