Question

Xt = 2 + Wt - 0.5Wt-1, t= 1,2, 3 .... where Wt ~ i.i.d N(0,9)...

Xt = 2 + Wt - 0.5Wt-1, t= 1,2, 3 ....

where Wt ~ i.i.d N(0,9)

Compute E(Xt) and var(Xt)

Find correlation of Xt and Wt-1

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Please take care of one thing here. Generally when we say X follows normal distribution , we read it as X~N(mu, sigma^2)

Here I have taken 9 as sigma^2 for Wt

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Consider the series xt = −.8xt−2 + wt and yt = 2cos(2πt) + wt, where wt...
Consider the series xt = −.8xt−2 + wt and yt = 2cos(2πt) + wt, where wt ∼ iid N(0,1). Determine each of the following functions: (b) the autocovariance functions γx(s, t) and γy(s, t) (c) the autocorrelation functions ρx(s, t) and ρy(s, t)
Calculate the spectral density of model Xt = 0.5Xt−1+wt+0.5wt−1 where wt is the white noise with...
Calculate the spectral density of model Xt = 0.5Xt−1+wt+0.5wt−1 where wt is the white noise with variance 1.
Using R statistical software (a) Generate n = 100 observations from following time series model xt...
Using R statistical software (a) Generate n = 100 observations from following time series model xt =2cos(2πt/4)+ωt, where ωt is i.i.d N(0,1). (b) Apply the moving average to xt and get time series yt, such that yt = (xt + xt−1 + xt−2 + xt−3)/4. [hint: Use filter(x,rep(1/4,4)),sides=1] (c) Plot xt as a line and superimpose yt as a dashed line. (d) Describe the relationship between xt and yt.
X1, … Xn are i.i.d. random variables, and E(Xi ) = 3β, Var(Xi ) = 3β^2...
X1, … Xn are i.i.d. random variables, and E(Xi ) = 3β, Var(Xi ) = 3β^2 , i = 1 … n, β > 0. Two estimators of β are defined as β̂ 1 = (X̅ /3) β̂ 2 = (n /3n+1 ) X̅ Show that MSE(β̂ 2) < MSE(β̂ 1) for a sample size of n = 3.
a) Let Xi for i = 1,2,...n be random variables with E[Xi] = μi (not necessarily...
a) Let Xi for i = 1,2,...n be random variables with E[Xi] = μi (not necessarily independent). Show that E[∑ni =1 Xi] = [∑ni =1 μi]. Show from Definition b) Suppose that random variables Yi for i = 1, 2,...,n are independent and identically distributed withE[Yi] =γ(gamma) and Var[Yi] = σ2, Use part (a) to show that E[Ybar] =γ(gamma). (c) Suppose that random variables Yi for i = 1, 2,...,n are independent and identically distributed with E[Yi] =γ(gamma) and Var[Yi]...
g(s,t)=f(x(s,t),y(s,t)) where f(x,y)=x^2-xy^3, x(3,4)=2, y(3,4)=-2, xs(3,4)=4 xt(3,4)=-1, ys(3,4)=10, and yt(3,4)=-100. Calculate gs(3,4)
g(s,t)=f(x(s,t),y(s,t)) where f(x,y)=x^2-xy^3, x(3,4)=2, y(3,4)=-2, xs(3,4)=4 xt(3,4)=-1, ys(3,4)=10, and yt(3,4)=-100. Calculate gs(3,4)
Consider the following difference equation for populations called the nonlinear logistic model ?t+1=?xt(1−xt) (a) Find the...
Consider the following difference equation for populations called the nonlinear logistic model ?t+1=?xt(1−xt) (a) Find the equilibria. Here ?>0 is an unknown parameter (i.e., is a constant). (b) Determine the values of r for which each equilibrium is stable.
Q2)a) Find the trigonometric Fourier series coefficients of the following signal xt=3+4Sin3(10t) b) Draw the signal...
Q2)a) Find the trigonometric Fourier series coefficients of the following signal xt=3+4Sin3(10t) b) Draw the signal defined below and find the trigonometric Fourier series representation of the signal xt=n=-∞∞3(-1)nδ(t-4n)
Consider the AR(2) process given by Xt – Xt-1 + 0.25Xt-2 = et. Find the first...
Consider the AR(2) process given by Xt – Xt-1 + 0.25Xt-2 = et. Find the first five ACF's of the process. Please post with steps!
Determine the interval(s) where r(t)=< t-1/((t^2) -1), 2e^3t , In(t+5) > is continuous. And Both r1(t)...
Determine the interval(s) where r(t)=< t-1/((t^2) -1), 2e^3t , In(t+5) > is continuous. And Both r1(t) = < t2, t4 > and  r2(t) = < t4, t8 > map out the same half parabolic graph. Notice that both r1(1) = < 1, 1 > and  r2(1) = < 1, 1 >. However, r'1(1) = < 2, 4 > and  r'2(1) = < 4, 8 >. Explain why the difference is logical and quantify the difference at t=1. Determine the interval(s) where r(t)=<t −...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT