Question

In: Statistics and Probability

Let Zt = U sin(2*pi*t) + V cos(2*pi*t), where U and V are independent random variables,...

Let Zt = U sin(2*pi*t) + V cos(2*pi*t), where U and V are independent random variables, each with
mean 0 and variance 1.
(a) Is Zt strictly stationary?
(b) Is Zt weakly stationary?

Solutions

Expert Solution

orchestra answered 1 year ago
Next > < Previous

Related Solutions

If u(t) = < sin(8t), cos(4t), t > and v(t) = < t, cos(4t), sin(8t) >,...
If u(t) = < sin(8t), cos(4t), t > and v(t) = < t, cos(4t), sin(8t) >, use the formula below to find the given derivative. d/(dt)[u(t)* v(t)] = u'(t)* v(t) + u(t)*  v'(t) d/(dt)[u(t) x v(t)] = <.______ , _________ , _______>
If u(t) = < sin(5t), cos(5t), t > and v(t) = < t, cos(5t), sin(5t) >,...
If u(t) = < sin(5t), cos(5t), t > and v(t) = < t, cos(5t), sin(5t) >, use the formula below to find the given derivative. d/dt[ u(t) * v(t)] = u'(t) * v(t) + u(t)* v'(t) d/dt [ u(t) x v(t)] = ?
2. Let {Zt , t = 0, ±1, ±2, ...} be a sequence of independent random...
2. Let {Zt , t = 0, ±1, ±2, ...} be a sequence of independent random variables, each with mean EZt = 0 and variance Var(Zt) = σ 2 . Define Xt = ZtZt−1 + Zt−2. • Compute the mean and the covariance function for Xt . • Is {Xt} weakly stationary? Explain why.
Let U and V be independent continuous random variables uniformly distributed from 0 to 1. Let...
Let U and V be independent continuous random variables uniformly distributed from 0 to 1. Let X = max(U, V). What is Cov(X, U)?
Let {Zt} be independent normal random variables with mean 0 and variance σ2. Let a, b,...
Let {Zt} be independent normal random variables with mean 0 and variance σ2. Let a, b, c be constants. Which of the following processes are stationary? Evaluate mean and autocovariance function. (a) Xt = Ztcos(at) + Zt−1sin(bt) (b) Xt =a+bZt + cZt−2 (c) Xt = ZtZt−1
Define a random process by X(t) = Asin(50*pi*t)+B, where A and B are independent random variables,...
Define a random process by X(t) = Asin(50*pi*t)+B, where A and B are independent random variables, E(A) = 0, SD(A) = 4, E(B) = -3, SD(B) = 5. A. Determine the mean function of X(t) B. Determine the autocovariance function of X(t) C. determine the variance function of X(t) D. is X(t) wide-sense stationary? how can you tell?
Let (Un, U, n>1) be asequence of random variables such that Un and U are independent,...
Let (Un, U, n>1) be asequence of random variables such that Un and U are independent, Un is N(0, 1+1/n), and U is N(0,1), for each n≥1. Calculate p(n)=P(|Un-U|<e), for all e>0. Please give details as much as possible
Let U, V be iid Unif(0, 1) random variables, and set M = max(U,V) and N...
Let U, V be iid Unif(0, 1) random variables, and set M = max(U,V) and N = min (U,V) (a) Find the conditional density of N given M = a for any value of a ∈ (0, 1). (b) Find Cov(M, N).
use matlab y(t)=10*(cos(2*pi*500*t)+cos(2*pi*1000*t)+ cos(2*pi*1500*t)). e) Down sample y(t) by a factor of 6. Sketch the Fourier...
use matlab y(t)=10*(cos(2*pi*500*t)+cos(2*pi*1000*t)+ cos(2*pi*1500*t)). e) Down sample y(t) by a factor of 6. Sketch the Fourier transform with appropriate frequency axis. Check if all frequency components are correct? Up-sample the time-domain signal obtained in e) by a factor of 6. Use appropriate filter for interpolation. Sketch the Fourier transform of the up-sampled and filtered signal. Does the resulting signal show all frequency components of the original signal y(t)?
use matlab y(t)=10*(cos(2*pi*500*t)+cos(2*pi*1000*t)+ cos(2*pi*1500*t)). e) Down sample y(t) by a factor of 6. Sketch the Fourier...
use matlab y(t)=10*(cos(2*pi*500*t)+cos(2*pi*1000*t)+ cos(2*pi*1500*t)). e) Down sample y(t) by a factor of 6. Sketch the Fourier transform with appropriate frequency axis. Check if all frequency components are correct? Up-sample the time-domain signal obtained in e) by a factor of 6. Use appropriate filter for interpolation. Sketch the Fourier transform of the up-sampled and filtered signal. Does the resulting signal show all frequency components of the original signal y(t)?
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT