Find the PSD of a random process x(t) if E[x(t)] = 1 and Ryx(t) =1+ ea\t\.
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- Let Mx (t) = 1/(1-t), t < 1 be the moment-generating function of a random variable X. Find the moment-generating function of the random variable Y = 2X +1.The auto correlation function of a random process X(t) is R(T) = 3 + 2 exp(-4t²).Let u(X) be a nonnegative function of a random variable X. It can be shown that P(u(X) >= c) <= E(u(X)) / c Suppose X is a random variable with momonet generating function Mx(t). Show that P(X>= a) <= exp(-ta) * Mx(t) Thank you
- Find the PSD of a random process X(t) if E[X(t)] =1 and R(T) = 1 + e-aIt, X,2 Let X (t) be a random process with mean 3 and auto correlation R(t, t2) = 9 + 4 e-0.2 ,-t, Determine the mean, variance and covariance of the random variables Z =X (5) and wX (8).he life X (in years) of a voltage regulator of a car has the pdf f(x) = cx²e-()³, x>0 (b) Find IQR. (a) Find c. (c) Given that it has lasted at least 7 years, what is the conditional probability that it will last at least another 3.5 years? If the moment-generating function of a random variable W is M(t) = (1 - 7t)-20, find the pdf, mean, variance, and mode of W.
- Find E(R) and V (R) for a random variable R whose moment-generating function ismR(t) = e2t(1-3t2)-1Let m(t) be the moment generating function of a random variable X. Show that the random variable W = 10X is m(10t). What is the moment generating function of Z = X-5 in terms of m(t)?A stationary unity mean random process X (t) has the auto correlation function RYy (T) = 1 + e 2, Find the mean and variance ofY= 1 x (t) · dt
- Consider the random process W(t) = X cos(2π fot) + Y sin(2π fot) where X and Y are uncorrelated random variables, each with expected value 0 and variance o². (a) Find the auto-correlation function of the random process W(t). (b) Is W (t) wide sense stationary (WSS) ?Let X and Y be independent random variables, prove that Var (XY) = Var (X) Var (Y) if E [X] = E[ Y] = 0.The autocorrelation function of a stationary random process X(t) is given by 16 Rxx (T) = 36+ 1+87² Find the mean, mean square and variance of the process.