Answers
| a) E(X)= ∫2132∫2132 kx(x2+y2) dx dy = | 26.8751 | =E(Y) | |||
| E(X2)= ∫2132∫2132 kx2(x2+y2) dx dy = | 732.2716 | ||||
| Var(X)=E(X2)-(E(X))2 = | 9.9997 | =VAR(Y) | |||
| E(XY)= ∫2132∫2132 kxy(x2+y2) dx dy = | 722.1312 | ||||
| a) therefore Cov(X,Y)=E(XY)-E(X)*E(Y)= | -0.1407 | ||||
| and b) correlation coefficient ρ =Cov(X,Y)/(σx*σy)= | -0.0141 | ||||
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