Let n have a bin(100, 1/4) distribution. given that n = n flip a fair coin n times and let x be the number of heads observed. (a) what is the distribution of x given n = n. be sure to provide a range and a proper conditional probability mass function. (b) find the random variable e(x|n). (c) using part (b), compute e(x). (if you do not use part (b), and instead just give an educated guess, you will receive zero points.)