che random binary transmission process {X(t)} is a WSS process with zeromean and autocorrelation function R(T) = 1Twhere T is a constant. Find-the mean and variance of the time average of {X(t)} over (0, T). Is {X(t)} meanergodic?

Answered: Image /qna-images/answer/789ddce5-e5b0-4654-8061-3f08fdaa7ff4.jpg

Answered: "The randoffI ualisimission process…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 25EQ

See similar textbooks

Similar questions

13) Random variables X and Y have joint pdf fXY={4xy, 0≤x≤1, 0≤y≤1fXY={4xy, 0≤x≤1, 0≤y≤1 Find Correlation and Covariance
Probability and Stochastic Process Identify for the following 13.3 13.4 13.5 13.6 whether the process is discrete time or continuous time, discrete or continuous value
X1 and X2 are two discrete random variables, while the X1 random variable takes the values x1 = 1, x1 = 2 and x1 = 3, while the X2 random variable takes the values x2 = 10, x2 = 20 and x2 = 30. The combined probability mass function of the random variables X1 and X2 (pX1, X2 (x1, x2)) is given in the table below a) Find the marginal probability mass function (pX1 (X1)) of the random variable X1.b) Find the marginal probability mass function (pX2 (X2)) of the random variable X2.c) Find the expected value of the random variable X1.d) Find the expected value of the random variable X2.e) Find the variance of the random variable X1.f) Find the variance of the random variable X2.g) pX1 | X2 (x1 | x2 = 10) Find the mass function of the given conditional probability.h) pX2 | X1 (x2 | x1 = 2) Find the mass function of the given conditional probability.i) Are the random variables X1 and X2 independent? Show it. The combined probability mass function of the random variables X1 and X2 is below
continuous random variables Z is known to have an Erlang (2,1.3) type PDF. what is the variance of Z ?
A stochastic process (SP) X(t) is given byX(t) = Asin(ωt + Φ)where A and Φ are independent random variables and Φ is uniformly distributed between 0 and 2π.a) Calculate mean E[X(t)]. b) Calculate the auto-correlation RX (t1,t2).c) Is X(t) wide sense stationary (WSS)? Justify your answer.Now consider that X(t) is a Gaussian SP with mean μX (t) = 0.5 and auto-correlation RX (t1,t2) =10e−14 |t1−t2|. Let Z = X(5) and W = X(9) be the two random variables.d) Calculate var(Z), var(W), and var(Z + W). e) Calculate cov(ZW).
1)Let x be a random variable Gaussian with zero mean and variance 1. Find:a)The conditional pdf and pdf of x given x > 0;b)E [ x| x>0 ]c)Var [ x | x >0]
A simple random sample X1, …, Xn is drawn from a population, and the quantities ln X1, …, ln Xn are plotted on a normal probability plot. The points approximately follow a straight line. True or false: a) X1, …, Xn come from a population that is approximately lognormal. b) X1, …, Xn come from a population that is approximately normal. c) ln X1, …, ln Xn come from a population that is approximately lognormal. d) ln X1, …, ln Xn come from a population that is approximately normal.
X = max(10,Y) with Y ~ Poisson(lambda=13) a) Calcuate the exact expectation and the variance of X.
Economics Now suppose that the time series process {Xt}, is expressed as Xt = z + et where et is iid with a mean of zero and a variance of σ , and the variable z does not change over time (time invariant) which means it has a mean E(z) = 0 and , and it is assumed that z and et are uncorrelated: i. Find the mean xt , E(Xt) and the variance Xt, var(Xt). Do they depend on t? ii. Determine the covariance of xt and xt+h for h > 0, Cov(Xt , xt+h) iii. Is xt stationary? Explain.
Draw a scatter diagram for the data and determine by inspection if there exists an approximate linear relationship between Y and X. Approximately draw a straight-line between the plotted values. State the general relationship between Y and disposable X in1.exact linear form 2. stochastic form.
If X is a random variable with expectation µ and variance cµ2 , where c is a constant. Find a variance stabilizing transformation of X.
Let Z~Normal(0,1). Define X1 = Z and X2 = Z^2. Calculate the correlation coefficient ofPearson's correlation coefficient.Hint 1: For Pearson's correlation coefficient, it is possible to use the property of the symmetry of the normal distribution.symmetry of the normal distribution, or equivalently in terms of calculus, the properties of integrals for odd functions.properties of the integrals for odd functions. In this way, it will not be necessary tosolve integrals that have no solution in the form of an easy to work with function. Hint 2: The way I found to calculate both Kendall's and Spearman's coefficients was to calculate the probability P[(X1 - X1).Spearman coefficients, was to calculate the probability P[(X1 - X1′)(X2 - X2′) > 0] and substituting it into theforms equivalent to the definition that come in the book. The one that seems simplest to meis to substitute the X's by their corresponding Z's and use remarkable products to arrive at aprobability in terms of a normal…

SEE MORE QUESTIONS

Recommended textbooks for you

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

"The randoffI ualisimission process {X(t)} is a WNSS process with zero | where T is a constant. Find T mean and autocorrelation function R(T) = 1– the mean and variance of the time average of {X(t)} over (0, T). Is {X(t)} mean ergodic?