2. (a) When two random variables (X, Y) follow a bivariate normal distribution, thecovariance matrix Σ is defined asΣρσισ2(010₂ Posts),-=where p is the correlation, o, o are the variances of X and Y respectively. Use mvrnormfrom the MASS library (use library(MASS)) to generate 100 samples from a bivariate normalCall the first column xdistribution 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 (usecor) and compare with the population correlation p. (First work out p in the Σ given.)

Answered: Image /qna-images/answer/f7af49b1-40fb-429e-b2ef-42db4146cc03.jpg

Answered: 2. (a) When two random variables (X, Y)…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Let X1, X2, X3, ..., X, be a random sample from a distribution with known variance Var(X,) = o², and unknown mean EX, = 0. Find a (1 – a) confidence interval for 0. Assume that n is large.

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