## Answers

a) E(X)= ∫_{21}^{32}∫_{21}^{32} kx(x^{2}+y^{2}) dx dy = | 26.8751 | =E(Y) | |||

E(X^{2})= ∫_{21}^{32}∫_{21}^{32} kx^{2}(x^{2}+y^{2}) dx dy = | 732.2716 | ||||

Var(X)=E(X^{2})-(E(X))^{2} = | 9.9997 | =VAR(Y) | |||

E(XY)= ∫_{21}^{32}∫_{21}^{32} kxy(x^{2}+y^{2}) 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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