3. Conditioning on a random variable (10 points). Let the r.v. N be the outcome of a biased 4 sided die roll and assume that it has the pmf PN(n) n 10 for n = 1, 2, 3, 4.F(X) 3/4 1/2 1/4 X -2 -1 2 3 Figure 1: Cdf of mixed r.v.. Given N = n, a coin with bias p = (n + 1)/2n is flipped. Let X be a r.v. that takes the value 1 if the outcome of the coin flip is heads and 0 if it is tails. Find the conditional expectation E(N | X) as a function only of X