Hi! I appreciate your help with the result and approach for these questions. Thanks!

Mid Term due Jul 20, 2021 18:59 COT Problem 4(a) 2 points possible (graded. results hidden) A random variable X is generated as follows. We flip a coin. With probability p, the result is Heads, and then X is generated according to a PDF which is uniform on 10, II. With probability I p the result is Tails, and then X is generated according to a PDF Of the form fxlT (x) = 22', (The PDF is zero everywhere else.) if x E (0, 1). I. What iS the (unconditional) PDF fx Of X? 2. calculate E Problem 4(b) 2 points possible (graded. results hidden) We now wish to estimate the result of the coin toss, based on the value of X. 1. Find P (TailslX 1/4). P (TailslX 1/4) 2. The MAP rule decides in favor of Heads if X < a and in favor of Tails if X > a. What is a?