Find the PSD of a random process x(t) if E[x(t)] = 1 and Ryx(t) = 1 + e-alt|
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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.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).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.
- 16) A stationary random process has an autocorrelation function of Rx (T)=16-e cos 20rt+8 cos10TT. Find the variance of this process.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) · dtLet N(t) be the percentage of a state population infected with a flu virus on week t of an epidemic. What percentage is likely to be infected in week 4 if N(3) = 8 and N'(3) = 1.2?
- A random process X(t) is applied as input to a system whose impulse response is h(t) 3u(t)t² exp (-8t). If E[X(t)] = 2, what is the mean value of the system response y(t). - CS Scanned with CamScannerA (t) is a random process having mean = 2 and auto correlation function Rxx (7) = 4 [e- 0.2 ld+ 1. Let Y and Z be the random variables obtained by sampling X (t) at t = 2 and t = 4 respectively. Find the variance of the random variable W = Y -Z.Consider a random process x(t) = Acos(@t+0), where and are constants and 4 is a random variable with zero mean and variance o². Determine whether x(t) is a wide sense stationary process or not.
- 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) ?Find the PSD of a random process X(t) if E[X(t)] =1 and R(T) = 1 + e-aIt, X,X (t) is a random process having mean = 2 and auto correlation function. Rxx (7) = 4 [e-0.2 ltl + 1. Let Y and Z be the random variables obtained by sampling X (t) att = 2 and t = 4 respectively. Find the variance of the random variable W = Y -Z.