Consider the joint probability distribution below. Complete parts (a) through (c

Question

Consider the joint probability distribution below. Complete parts (a) through (c). 2 0.80 0,00 0.00 0.20 a. Compute the marginal probability distributions for X and Y. 2 0.00 0.20 P(y) 0.80 0.00 P(x) Type integers or decimals.) b. Compute the covariance and correlation for X and Y. Cov(XY)- (Type an integer or a decimal.) Corrx) (Round to three decimal places as needed.) c, compute the mean and variance for the linear function w = 6x-9Y. w = [ (Type an integer or a decimal.) = (Round to four decimal places as needed.) Enter your answer in each of the answer boxes. Save for Later

Explanation / Answer

bold digits are answers for part a

(b)

cov(x,y)=E(xy)-E(x)E(y)=0*1*0.8+0*2*0+1*1*0+1*2*0.2-(1*0.8+2*0.2)*(0*0.8+1*0.2)=0.16

(c)

V(X)=1*0.8+22*0.2-1.22=0.36

V(Y)=1*0.2-0.22=0.16

corr(x,y)=cov(x,y)/(squareroot(V(x)V(y))=0.667

(c)

E(W)=6E(X)-9E(Y)=6*1.2-9*0.2=5.4

V(W)=36V(X)+81V(Y)-2*6*9cov(X,Y)=8.64

X 0 1 P(y) Y 0 0.8 0.0 0.8 1 0.0 0.2 0.2 P(x) 0.8 0.2 1

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