TYPO: Here R0, R1, R2 represent the received signal on the THREE frequencies.

A communication system transmits a hit [i] or I} of information by transmitting a signal on four differEnt frequencies. The received signal strength is diEerent on the four frequencies and is described as follows. Ru = 35c + Ti] H] = 351 + 7]] R2 = 332 + 1'32 I Here Ru, R1, R2 represent the received signal on the four frequencies. I The random variable B is either +1 or 1 depending on the bit. For example if the information bit is Ill then B = +1 whereas if the information bit is 1 then B = 1. I The variables rm, 1;], \"5'2: represent random (Gaussian or normal} noise with mean i] and variance of... The noise \"TD: in, and 132 are independent. I The receiver combines the received signals as R = chq +na1R1 + 11232 and then compares R with ll. The receiver's decision for B is called B. If R 'e U the receivEr decides that B = +1. If R E I] the receiver decides B = 1. I The goal of the receiver is to decide correctly the data. Of course it is possible that because of noise, the decision is incorrect and we say an error occurred. {a} DeteHnine the conditional mean of R givm B = +1 as a function of (1-11,,[1151'12 and an, s1, 52. {b} Determine the conditional variance of R given 3 = +1 as a function of an, al, a2 and 55, s1, as. (c) Determine the conditional density of R given 3 = +1 as a function of am I1, as and 5a: 51: 52- (d) Determine the conditional Izirobahihtg.r of error givan B = +1 as a function of on, [homag and su, 51,52... The answm' should he in tarms of the 1:! function