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03) Assume that we have a-N (al 1,.2) b-N(b11.4) and that a and b are independent. a)What is the pdf0f :-3a+5b ? b) Now suppose that a and b are correlated such that the jointly normal pof is given as Recalculate the pdf of z with the added correlation. c) yse the mvnmdü routine in the Matlab statistical toolbox to generate a m the correlated components of a and b. Verify that for large number of random samples that the mean and variance converges to the theoretical values given in part bQ3) Assume that we have a N(a|1,2) b N(bl11,4) and that a and b are independent. a) What is the pdf of z 3a+5b? b) Now suppose that a and b are correlated such that the jointly normal pdf is given as Recalculate the pdf of z with the added correlation. c) Use the mvnrnd() routine in the Matlab statistical toolbox to generate a monte-carlo simulation of z from the correlated components of a and b. Verify that for large number of random samples that the mean and variance converges to the theoretical values given in part b.

yes mean is 1 and variance is 2.

math   Statistics-And-Probability   
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Answer #1

ag b ake independent 5b N (55, l00 (3 5)(b)NH 4a: (S 5) ()355 53 33十115 ユ148 (3 5) 9 3415bN(58, 148)

>> y=mvnrnd(58,148,1000);
>> mean(y)

ans =

58.3996

>> var(y)

ans =

128.7465

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