For the probability distribution Then the Var ( X ) is (Given : .(0.25)^2=0.0625,(0.35)^2=0 1225,(0.45)^2=0 2025 )

Step-by-step solution

aligned E(X)= & (-2)(0.1)+(-1)(0.2)+0(0.2)+(1)(0.3) & +2(0.15)+3(0.05) = & -0.2-0.2+0+0.3+0.3+0.15 = & 0.35 aligned aligned Var ( X ) & = E ( X ^2 )-[ E ( X )]^2 & =(-2)^2(0.1)+(-1)^2(0.2)+0^2(0.2) & +1^2(0.3)+2^2(0.15)+3^2(0.05)-(0.35)^2 & =0.4+0.2+0+0.3+0.6 aligned aligned & =1.95-(0.35)^2 & =1.95-0.1225 & =1.8275 aligned