PROBLEM7 X (t) is a random process having mean= 2 and auto correlation functionRYx (7) = 4 [e-0.2 ldLet Y and Z be the random variables obtained by sampling X (1) at t = 2 and t =4 respectively. Find the variance of the random variable W = Y -Z.%3D

Answered: Image /qna-images/answer/910540ba-1970-425d-97d8-4f8b96c08af6.jpg

Answered: PROBLEM 7 X (t) is a random process…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

Example 11. Find the mean values of two random variables x and y and the correlation coefficient between them when the two lines of regression are given by: 5x + 7y – 22 = 0 and 6x + 2y – 20 = 0. If the variance of y is 15, find the standard deviation of x. -
If var(X) = var(Y) = σ², cov(X,Y)= and 2Y-3 find the correlation between 2X+3
Example 10-3. Show that if X', Y’ are the deviations of the random variables X andY from their respective means, then 1 (1) r =1- 2N X'; Y;\ Ox Oy,
4. Question 4: Y is a discrete random variable with PMF S1/3, y=1 p(y) = 2/3, y = 2 (a) Find the MGF for Y. (b) Develop the first two raw moments from MGF and find the variance V(Y). Answers:
1.
If var(X) = var(Y) = σ², cov(X,Y)= and 2Y-3 find the correlation between 2X+3
13-20. If V(X) = V(Y) = 7 and V (X - Y) = the correlation coefficient between random %3D variable X and Y is (i) -: (ii)} ;
2
18. Two random variables have the regression equations : 3 X+2Y - 26 = 0 6X+ Y- 31 = 0 Find the mean value and the coefficient of correlation between X and Y. If the variable of X 25, find the standard deviation of Y from the data given above. tem (be scue)
6. Show that 1 s2 E1(Xi – x)² is unbiased estimator of the population variance o? i=1 п-1
2. (a) When two random variables (X, Y) follow a bivariate normal distribution, the covariance matrix Σ is defined as Σ ρσισ2 (010₂ Posts), - = where p is the correlation, o, o are the variances of X and Y respectively. Use mvrnorm from the MASS library (use library(MASS)) to generate 100 samples from a bivariate normal Call the first column x distribution with μ = (₁, ₂) with μ₁ = (11). 2,42 = 3, and Σ = = and the second column y. (b) Plot the histogram of x and overlay it with the corresponding marginal normal density. Repeat for y. (Recall the marginal distribution of X is N (μ₁, 0²).) (c) Produce a scatter plot of x and y (use plot). Compute the sample correlation coefficient (use cor) and compare with the population correlation p. (First work out p in the Σ given.)
5. (a) Establish the formula: nroxdy = n,r,0x, Oy, + n2r20x,Oy, + n,dx,dy, + nzdx,dy2 Where dx, = x - i, dy, = 91 - y, dx, = X2 - X, dy, = y2 - y 5. (b) Find the correlation coefficient of combined sample given that %3D %3! Sample Size Mean of X Var(X) Mean of Y Correlation between X and Y Var(Y) Group 1 n = 100 i, = 80 ox? = 10 y, = 100 o = 15 %3! = 0.6 Group 2 n2 = 150 = 72 Ox = 12 y, = 118 o = 18 2 = 0.4

Recommended textbooks for you

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

Elementary Statistics: Picturing the World (7th E…

Statistics

ISBN:

9780134683416

Author:

Ron Larson, Betsy Farber

Publisher:

PEARSON

The Basic Practice of Statistics

Statistics

ISBN:

9781319042578

Author:

David S. Moore, William I. Notz, Michael A. Fligner

Publisher:

W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:

9781319013387

Author:

David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:

W. H. Freeman

SEE MORE TEXTBOOKS

PROBLEM 7 X (t) is a random process having mean = 2 and auto correlation function Rxx (t) = 4 [e-0.2 Id + 11. Let Y and Z be the random variables obtained by sampling X (t) at t = 2 andt = 4 respectively. Find the variance of the random variable W = Y -Z.