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 do not repost response from other post.

A binary erasure channel has binary input X E {0, 1} and ternary output Y E {0, 1, 2} (see the probability transition diagram below). The erasure, represented by 2, corresponds to the case when the receiver cannot deter- mine whether the received signal is a O or a 1. When a 0 is sent, a 0 is received with probability 0.9, i.e., py1x(0|0) = 0.9, and a 2 is received with probability 0.1. When a 1 is sent, a 1 is received with probability 0.8 and a 2 is received with probability 0.2. In answering the following questions, assume that X ~ Bern(l/3). 0 0.9 0 0.1 X 2 Y 0.2 1 0.8 1 (80 Find pan/(:12, y), ram/(y), and pxiytvly) for y = 0,112- (b) Find the error probability P3 = P{X 7E Y}. (0) Now, suppose we use the MAP rule to estimate X by X E {0,1}. What is the probability of decoding error, i.e., PU? 75 X }? Compare this probability of error to that without decoding