Problem 4: Let X(t) be a random process as: X(t) = cos(2лft+), where is a random variable distributed uniformly over (0, 2). This means that its PDF is 1 for Є[0,2] fo()=2π 0 otherwise (a) Determine the expectation of X(t), mx(t). (b) Determine the autocorrelation function of X(t), Rx(t,t+t). (c) Is X(t) a wide sense stationary (WSS) process? Explain why. (d) Determine the power spectral density (PSD) of X(t), Sx(f).

F(A, B,C, D) =) (3,6, 7, 10, 11, 12, 14) How many equal alternative minimizations this function has?

A continuous random variable X has pdf: p(x) = { kx 0 < x < 1, 0 otherwise Find: a) the constant k. b) CDF F(x). c) P(1

The signal x(t) is band-limited to 40 Hz and is modulated with a 320 Hz carrier, which generates y(t). This signal is then processed by a quadratic-law device that produces the output g(t) = y²(t). a) What is the minimum sampling rate for x(t) that avoids aliasing?b) What is the minimum sampling rate for y(t) that avoids aliasing?c) What is the minimum sampling rate for g(t) that avoids aliasing?

2. Find the minimum product of sums for: F(A,B,C,D,E)= m(0, 1, 2, 6, 7, 9, 10, 15, 16, 18, 20, 21, 27, 30)+E d(3, 4, 11, 12, 19)

2) A joint pdf is described below. A new random variable is formed as shown: W=Y+X. Determine an expression for the CDF for W. Please solve all integrals -4 y 4 -4 4 X 1 128 0 fxy(x, y) 2-1 = −4 < y < 4, −4 < x < 4 y<-x otherwsie

let us say we are given ZA and Z'B and those two are prime implicants of a specific function. The Z standing for a variable, while the A and B are both two product terms. Consider A*B does not equal to zero, Is their consensus AB an implicant? Also is it a prime implicant? If the answer is yes a prime implicant then prove it. If the anwer is no not a prime implicant give a counterexample to show the opposite.

For the function f(a,b,c,d)= Em(0,1,3,5,6,7,8,10,14,15), find all minimum sum-of-products solution, using the Quine-McCluskey method.

DIGITAL COMMUNICATION

not use ai please