4. (25%) Consider the output of an envelope detector given by y(t) = {[Ac+ Ackam(t) + ni(t)] + n(t)}1/2 where A is a Bernoulli random variable taking values of +1 and -1. We know P[A = 1] = q and PA -1] = 1-q. (a) Assume that the probability of the event no(t)> A(1+m(t)), < <1, is equal to or less than 61, whereas the probability of the event no(t)>A.(1-m(t))\, <1, is equal to or less than 82. If we consider these two events are exclusive, what is the probability that the effect of the quadrature component no(t) is negligible? (b) Suppose the probability of the event A.[1+m(t)]+ni(t) < 0 is equal to 63 and the probability of the event A.[1-m(t)] + ni(t) < 0 is equal to 64. Consider these two events are exclusive and find the probability that the following approximation is valid. y(t) Ac[1+kam(t)] + n,(t)