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A random process X(t) is given by: X(t)= K cos(2 tt) ,t20 w is constant and...
2. Consider the random process x(t) defined by x(t) a cos(wt + 6).where w and a are constants, and 0 is a random variable uniformly distributed in the range (-T, ) Sketch the ensemble (sample functions) representing x(t). (2.5 points). a. b. Find the mean and variance of the random variable 0. (2.5 points). Find the mean of x(t), m (t) E(x(t)). (2.5 points). c. d. Find the autocorrelation of x(t), R (t,, t) = E(x, (t)x2 (t)). (5 points)....
2. Consider the random process x(t) defined by x(t) a cos(wt 6), where w and 0 are constants, and a is a random variable uniformly distributed in the range (-A, A). a. Sketch the ensemble (sample functions) representing x(t). (2.5 points). b. Find the mean and variance of the random variable a. (5 points). c. Find the mean of x(t), m(t) E((t)). (5 points). d. Find the autocorrelation of x(t), Ra (t1, t2) E(x (t)x2 )). (5 points). Is the...
ne 10. 2019 4. A random process Z(t) is given by, Z(t) = Kt, where K is a random variable The probability dessity function for K is given below. Use this information to answer the questions below (20 points k <-1 0 fK(k)=-k-1sks k> 1 0 (a) Find the mean function for Z(t). (b) Find the autocovariance function for Z(e). (c) Is this process wide sense stationary (WSS)? Explain your answer in 2-3 sentences. ne 10. 2019 4. A random...
The sample function X(t) of a stationary random process Y(t) is given by X(t) = Y(t)sin(wt+Θ) where w is a constant, Y(t) and Θ are statistically independent, and Θ is uniformly distributed between 0 and 2π. Find the autocorrelation function of X(t) in terms of RYY(τ).
Let a random process x(t) be defined by x(t) = At + B (a) If B is a constant and A is uniformly distributed between-1 and +1, sketch a few sample functions (b) If A is a constant and B is uniformly distributed between 0 and 2, sketch a few sample functions c) Evaluate (r2(t)) d) Evaluate x2(t) e) Using the results of part c) and d), determine whether the process is ergodic for the averages Let a random process...
Consider a random process X(t) defined by X(t) - Ycoset, 0st where o is a constant 1. and Y is a uniform random variable over (0,1) (a) Classify X(t) (b) Sketch a few (at least three) typical sample function of X(t) (c) Determine the pdfs of X(t) at t 0, /4o, /2, o. (d) EX() (e) Find the autocorrelation function Rx(t,s) of X(t) (f) Find the autocovariance function Rx(t,s) of X(t) Consider a random process X(t) defined by X(t) -...
A random variable X is uniformly distributed on the interval [-TT/2.TT/2]. X is transformed to the new random variable Y = T(X) = 2 tan(X). Find the probability density function of Y. (Hint: (tan x)' = 1/cos2x, cos?(tan 1x) = 1/(1+x2)
and is X(t) a WSS process? 6.11 Sinusoid with random phase. Consider a random process x(t)-A cos(wot + ?), where wo are nonrandom positive constants and o is a RV uniformly distributed over A and (0, ?), i.e., ? ~11(0, ?). (a) Find the mean function 2(t) of X(t).
Three random variables A, B, and C and 1. The random processes X(t) and Y (t) answer the questions below. (24 points) independent identically distributed (id) uniformly between are defined by the given equations. Use this information to are X(t) = At + B Y(t) = At + C (a) Find the autocorrelation function between X(t) and Y(t) (b) Find the autocovariance function between X (t) and Y(t). (c) Are X(t) and Y(t) correlated random processes? Three random variables A,...
Please answer all the questions thank you ne 10. 2019 4. A random process Z(t) is given by, Z(t) = Kt, where K is a random variable The probability dessity function for K is given below. Use this information to answer the questions below (20 points k <-1 0 fK(k)=-k-1sks k> 1 0 (a) Find the mean function for Z(t). (b) Find the autocovariance function for Z(e). (c) Is this process wide sense stationary (WSS)? Explain your answer in 2-3...