True/False questions . Here X and Y are two random variables and p(x, y) is their joint density. Also, p(x|y) = p(x,y)/p(y) and p(y|x) = p(x,y)/p(x) where p(x) and p(y) are the marginalized densities of X and Y , respectively. (a) (True/False)FortwoeventsAandB,Pr(A)=Pr(A|B)Pr(B)+Pr(A|Bc)Pr(Bc). (b) (True / False) E(XY 2) = E(X)E(Y 2) if X and Y are independent. (c) (True / False) V (Y |X) is calculated as ? (y − μy)2p(y|x)dy where μY = E(Y ). (d) (True/False)E(X|Y)=?xp(y|x)p(x)dx. p(y) (e) (True / False) The skewness of the lognormal distribution is positive. (f) (True / False) The regression function r(x) = E(Y |X = x) minimizes E(E((Y − r(X))2)). (g) (True/False)Cov(X,Y)israndom. (h) (True / False) This test is challenging/difficult.
True/False questions . Here X and Y are two random variables and
p(x, y) is their joint density. Also, p(x|y) = p(x,y)/p(y) and p(y|x) = p(x,y)/p(x) where p(x) and p(y) are the marginalized densities of X and Y , respectively.
(a) (True/False)FortwoeventsAandB,Pr(A)=Pr(A|B)Pr(B)+Pr(A|Bc)Pr(Bc).
(b) (True / False) E(XY 2) = E(X)E(Y 2) if X and Y are independent.
(c) (True / False) V (Y |X) is calculated as ? (y − μy)2p(y|x)dy where μY = E(Y ).
(d) (True/False)E(X|Y)=?xp(y|x)p(x)dx. p(y)
(e) (True / False) The skewness of the lognormal distribution is positive.
(f) (True / False) The regression
r(X))2)).
(g) (True/False)Cov(X,Y)israndom.
(h) (True / False) This test is challenging/difficult.
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