The question is as the picture.

6. The random variable X(r), a function of the random variable O, uniform over the interval (-x, x), and is 0 outside the interval, is given by X(1) = cos(out + 9). X(r) is input to a differentiator whose impulse response is h(r) - 8(1). The output signal is the random variable Y(f). (a.) Calculate the power spectral density Sx(w). (b.) Calculate the autocorrelation function Rx(1,1) = E[X()X(12)]. (c.) Calculate the probability mass density function fx(x) at / = /1. (d.) Compare the probability mass density at / = 12 with its probability mass density at ( = /1. (c.) If X(r) is WSS, express the autocorrelation function in terms of r = 12 -11. (f.) Determine the autocorrelation function Ry (1.12). (g.) If Y(r) is WSS, express the autocorrelation function in terms of r = 12 -1, (h.) Compute the output power spectral density Sy(w)