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Unformatted text preview: ρ = . 2. ( a ) Find the mean and the variance of the monthly portfolio return. ( b ) Find the probability of a monthly loss of more than $100 on this portfolio. ( c ) Given that in a particular month a return on a unit of stock B was $2, ﬁnd the probability that the entire portfolio returned a loss. Further properties of the bivariate Gaussian distribution Let X and Y be jointly normal distribution with the means μ X and μ Y , variances σ 2 X and σ 2 Y , and correlation ρ . • Suppose that the correlation ρ = 0. Then the joint pdf f X,Y ( x,y ) = f X ( x ) f Y ( y ) and so X and Y are independent. Conclusion : For jointly normal random variables zero correlations imply independence. This is NOT true without the assumption of joint normality ....
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 '09
 SAMORODNITSKY
 Normal Distribution, $1, $2, $3, Multivariate normal distribution, Σy

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