Question

Suppose that X(n) is a discrete-time process with mean m(n)=3 and autocovariance function R(n1, n2) =...

Suppose that X(n) is a discrete-time process with mean m(n)=3 and autocovariance function R(n1, n2) = 4e−0.2|n2−n1|. Here n = 0, ±1, ±2, .... Determine the mean, the variance and the covariance of the random variables X(5) and X(8). Is the process stationary? Does the process have mean-ergodicity?

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

Homework Answers

Answer #1

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
R1 = m + N1, where N1 is a normal distribution with mean 0 and variance...
R1 = m + N1, where N1 is a normal distribution with mean 0 and variance σ^2. R2 = m + N2, where N2 is a normal distribution with mean 0 and variance σ^2. R1 and R2 are my results, m is my sensor measurement, and N1 and N2 are noises to the measurement. R1 and R2 are both scalar functions, N1 and N2 are independent, and both variances are assumed to be known. How do you combine the 2...
Find the moment generating function of each of the following random variables. Then, use it to...
Find the moment generating function of each of the following random variables. Then, use it to find the mean and variance of the random variable 1. Y, a discrete random variable with P(X = n) = (1-p)p^n, n >= 0, 0 < p < 1. 2. Z, a discrete random variable with P(Z = -1) = 1/5, P(Z = 0) = 2/5 and P(Z = 2) = 2/5.
For a discrete random variable X, its hazard function is defined as hX(k) = P(X =...
For a discrete random variable X, its hazard function is defined as hX(k) = P(X = k + 1 | X > k ) = pX(k) / 1 − FX(k) , where FX(k) = P(X ≤ k) is the cumulative distribution function (cdf). The idea here is as follows: Say X is battery lifetime in months. Then for instance hX(32) is the conditional probability that the battery will fail in the next month, given that it has lasted 32 months...
1. Given a discrete random variable, X , where the discrete probability distribution for X is...
1. Given a discrete random variable, X , where the discrete probability distribution for X is given on right, calculate E(X) X P(X) 0 0.1 1 0.1 2 0.1 3 0.4 4 0.1 5 0.2 2. Given a discrete random variable, X , where the discrete probability distribution for X is given on right, calculate the variance of X X P(X) 0 0.1 1 0.1 2 0.1 3 0.4 4 0.1 5 0.2 3. Given a discrete random variable, X...
Suppose we have the following probability mass function. X 0 2 4 6 8 F(x) 0.1...
Suppose we have the following probability mass function. X 0 2 4 6 8 F(x) 0.1 0.3 0.2 0.3 0.1 a) Determine the cumulative distribution function, F(x). b) Determine the expected value (mean), E(X) = μ. c) Determine the variance, V(X) = σ^2
A function f”R n × R m → R is bilinear if for all x, y...
A function f”R n × R m → R is bilinear if for all x, y ∈ R n and all w, z ∈ R m, and all a ∈ R: • f(x + ay, z) = f(x, z) + af(y, z) • f(x, w + az) = f(x, w) + af(x, z) (a) Prove that if f is bilinear, then (0.1) lim (h,k)→(0,0) |f(h, k)| |(h, k)| = 0. (b) Prove that Df(a, b) · (h, k) = f(a,...
suppose x is a continuous random variable with probability density function f(x)= (x^2)/9 if 0<x<3 0...
suppose x is a continuous random variable with probability density function f(x)= (x^2)/9 if 0<x<3 0 otherwise find the mean and variance of x
15.1The probability density function of the X and Y compound random variables is given below. X                         &nbsp
15.1The probability density function of the X and Y compound random variables is given below. X                                        Y 1 2 3 1 234 225 84 2 180 453 161 3 39 192 157 Accordingly, after finding the possibilities for each value, the expected value, variance and standard deviation; Interpret the asymmetry measure (a3) when the 3rd moment (µ3 = 0.0005) according to the arithmetic mean and the kurtosis measure (a4) when the 4th moment (µ4 = 0.004) according to the arithmetic...
Suppose that the joint probability density function of the random variables X and Y is f(x,...
Suppose that the joint probability density function of the random variables X and Y is f(x, y) = 8 >< >: x + cy^2 0 ≤ x ≤ 1, 0 ≤ y ≤ 1 0 otherwise. (a) Sketch the region of non-zero probability density and show that c = 3/ 2 . (b) Find P(X + Y < 1), P(X + Y = 1) and P(X + Y > 1). (c) Compute the marginal density function of X and Y...
Suppose the position vector for a particle is given as a function of time by r...
Suppose the position vector for a particle is given as a function of time by r (t) = x(t)î + y(t)ĵ, with x(t) = at + b and y(t) = ct2 + d, where a = 1.90 m/s, b = 1.50 m, c = 0.124 m/s2, and d = 1.08 m. (a) Calculate the average velocity during the time interval from t = 1.85 s to t = 4.05 s. (b) Determine the velocity at t = 1.85 s. Determine...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT