The input to a binary communication system, denoted by a random variable x, takes on one of the two values 0 or 1 with probabilities and . The behaviour of the communication system is modelled by P(Y = 1 |x = 1|) = and P(Y = 0|x = 0) = Find P(Y = 1)

Thermal noise is passed through an ideal low-pass filter having cut-off at f_{c} = ωHz. The auto correlation value of the noise at the output of the filter is given as