Hi please use the given information to answer each part of the problem and please include any drawing, or steps/formulas to improve my understanding of the problem if necessary. Thank you! Please DON'T repost response from other similar question posts. Will thumbs up for any helpful work! :)

Conditioning on a random variable Let the r.v. N be the outcome of a biased 4 sided die roll and assume that it has the pmf PN(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