4. Let X be the sent bit and Y the received bit in a binary communications channel. The joint probability distribution f(x, y) is given as: f(x,y) x=0 x=1 y=0 0.4 0.1 y=1 0.1 0.4 (a) Compute the numerical value of P(Y = 1|X = 0) (b) Compute the covariance of random variables X, Y. (c) When a single bit is sent and received, we say that an error has occurred if Y + X. If a 8-bit long message is sent over this communication channel, what is the probability that 1 or less errors will occur?