2. Consider two random variables X and Y. Let 'c' be a deterministic constant.3A) derive a simple expression for cov(X, cY) in terms of c and cov(X, Y).B) derive a simple expression for cov(X, X+Y) in terms of var(X) and cov(X,Y).C) Suppose the new random variables W=X and Z-X+aY. where 'a' is a deterministicconstant. Find the value of 'a' according the stochastic parameters of X and Y so thatW and Z are uncorrelated.

Applying the Covariance formula and then procedd...........

Answered: 2. Consider two random variables X and…

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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A possible important environmental determinant of lungfunction in children is the amount of cigarette smoking in thehome. Suppose this question is studied by selecting twogroups: Group 1 consists of 23 nonsmoking children 5−9years of age, both of whose parents smoke, who have a mean forced expiratory volume (FEV) of 2.1 L and a standard devia-tion of 0.7 L; group 2 consists of 20 nonsmoking children of comparable age, neither of whose parents smoke, who havea mean FEV of 2.3 L and a standard deviation of 0.4 L. *8.31 What are the appropriate null and alternative hypoth-eses to compare the means of the two groups? *8.32 What is the appropriate test procedure for the hy-potheses in Problem 8.31? *8.33 Carry out the test in Problem 8.32 using the critical-value method. *8.34 Provide a 95% CI for the true mean difference in FEVbetween 5- to 9-year-old children whose parents smoke andcomparable children whose parents do not smoke.*8.35 Assuming this is regarded as a pilot study, how many…
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