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Let Yį be the number of hours spent studying for a quiz. Let Y2 be the grade (nu- merically represented). Suppose the joint d

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Answer #1

for above distribution:

E(Y1) =\sumy1*P(y1,y2) =0*(1/9+2/9+1/9)+1*(1/9+2/9+0)+2*(2/9+0+0)=7/9

E(Y2)=\sumy2*P(y1,y2) =2*(1/9+1/9+2/9)+1*(2/9+2/9+0)+0*(1/9+0+0)=4/3

E(Y1Y2) =\sumy1y2*P(y1,y2) =2*0*1/9+2*1*1/9+2*2*2/9+1*0*2/9+1*1*2/9+1*2*0+0*0*1/9+0*1*0+0*2*0=4/3

therefore Cov(Y1,Y2) =E(Y1Y2)-E(Y1)*E(Y2) =(4/3)-(7/9)*(4/3)=8/27

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