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  3. numerical proof of var(x + y ) = σ 2 x + σ 2

Numerical proof of Var(X + Y ) = σ 2 X + σ 2 Y...

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Statistics

Numerical proof of Var(X + Y ) = σ 2 X + σ 2 Y + 2Cov(X, Y):

***Please use R commands, that is where my confusion lies***

2.1 State how you create a dependent pair of variables (X, Y),give Var(X), Var(Y ), Cov(X, Y ), and Var(X + Y ).

2.2 Choose a sample size n and generate (xi , yi), i = 1, . . ., n according to the (X,Y) distribution. Give the sample variancesof the x-sample and y-sample, the sample covariance of the(x,y)-sample, and the sample variance of the x+y sample.

2.3 Turn in all R commands and the output showing theresults.

Answer & Explanation Solved by verified expert
4.1 Ratings (604 Votes)
x rnorm100 x 1 139508770 123749355 089043356 044246252 048219278 051737739 7 043736545 144127576 069844128 130431716 173347160 064656737 13 031893521 054369421 035821053 011477235 272183527 007533421 19 107264450 004917985 045877550 009283623 081798545 125331236 25 001787277 152285714 012152447 070239760 140953925 089200808 31 025002911 071849054 001372816 127846813 065457045 156526313 37 113734122 116262413 130518708 226470247 004927437 059248387 43 070503592 038757838 077413858    See Answer
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