I want to know the answers and details step by stepThank you so much LetiidX₁, X2,..., Xnd fx(x; 0)where fx(x; 0) is some unspecified distribution, but we have the following information:E(X)Var(X)E(X³)E(X4)====010³ + 3004 +68² +3 2.For each of the following estimators, compute their bias and variance0 = -1+ Σ1.2.3.πX?02 - - 2x - xx - x2--i=1Îg = X

Given, X1, X2, . . ., Xn~iidfXx, θ EX=θ VarX=1 EX3=θ3+3θ EX4=θ4+6θ2+3 1. θ^1=-1+1n∑i=1nXi2 Eθ^1=E-1+1n∑i=1nXi2=E-1+E1n∑i=1nXi2=-1+1n∑i=1nEXi2=-1+1n∑i=1nVarXi+EXi2=-1+1n∑i=1n1+θ2=-1+1n×n1+θ2=-1+1+θ2=θ2 Bias=θ-Eθ^1=θ-θ2 Varθ^1=Var-1+1n∑i=1nXi2=Var-1+Var1n∑i=1nXi2=0+1n2∑i=1nVarXi2=1n2∑i=1nEXi4-EXi22=1n2∑i=1nθ4+6θ2+3-1+θ2=1n2×∑i=1nθ4+6θ2+3-1+2θ+θ2=1n2∑i=1nθ4+6θ2+3-1-2θ-θ2=1n2∑i=1nθ4+5θ2-2θ+2=1n2×nθ4+5θ2-2θ+2=1n(θ4+5θ2-2θ+2)2. θ^2=1n∑i=1nXi-X1-Xn2 Xi-X1-Xn2=Xi-X1+Xn2=Xi2-2XiX1+Xn+X1+Xn2=Xi2-2XiX1-2XiXn+X12+2X1Xn+Xn2=Xi2+X12+Xn2-2XiX1-2XiXn+2X1Xn EXi-X1-Xn2=EXi2+X12+Xn2-2XiX1-2XiXn+2X1Xn=EXi2+EX12+EXn2-2EXiEX1-2EXiEXn+2EX1EXn=1+θ2+1+θ2+1+θ2-2×θ×θ-2×θ×θ+2×θ×θ=31+θ2-2θ2=3+3θ2-2θ2=3+θ2 Eθ^2=E1n∑i=1nXi-X1-Xn2=1nE∑i=1nXi-X1-Xn2=1n∑i=1nEXi-X1-Xn2=1n∑i=1n3+θ2=1n×n3+θ2=3+θ2 Bias=θ-Eθ^2=θ-(3+θ2) Xi-X1-Xn4=Xi-X1+Xn4=Xi4-4Xi3X1+Xn+6Xi2X1+Xn2-4XiX1+Xn3+X1+Xn4=Xi4-4Xi3X1+Xn+6Xi2X12+2X1Xn+Xn2-4XiX13+3X12Xn+3X1Xn2+Xn3+X14+4X13Xn+6X12Xn2+4X1Xn3+Xn4=Xi4-4Xi3X1-4Xi3Xn+6Xi2X12+12Xi2X1Xn+6Xi2Xn2-4XiX13-12XiX12Xn-12XiX1Xn2-4XiXn3+X14+4X13Xn+6X12Xn2+4X1Xn3+Xn4 VarXi-X1-Xn2=EXi-X1-Xn4-EXi-X1-Xn22 EXi-X1-Xn4=EXi4-4Xi3X1-4Xi3Xn+6Xi2X12+12Xi2X1Xn+6Xi2Xn2-4XiX13-12XiX12Xn-12XiX1Xn2-4XiXn3+X14+4X13Xn+6X12Xn2+4X1Xn3+Xn4=θ4+6θ2+3-4θ3+3θθ-4θ3+3θθ+61+θ21+θ2+121+θ2×θ×θ+61+θ21+θ2-4θθ3+3θ-12θ1+θ2θ-12θ×θ1+θ2-4θθ3+3θ+θ4+6θ2+3+4θ3+3θθ+61+θ21+θ2+4θθ3+3θ+θ4+6θ2+3=3θ4+6θ2+3-8θθ3+3θ+181+θ21+θ2-121+θ2θ2=3θ4+18θ2+3θ-8θ4-24θ2+18+18θ4+36θ2-12θ2-12θ4=θ4+18θ2+3θ+18 VarXi-X1-Xn2=θ4+18θ2+3θ+18-3+θ22=θ4+18θ2+3θ+18-9+θ4+6θ2=θ4+18θ2+3θ+18-9-θ4-6θ2=12θ2+3θ+9 Varθ^2=Var1n∑i=1nXi-X1-Xn2=1n2∑i=1nVarXi-X1-Xn2=1n2∑i=1n12θ2+3θ+9=1n2×n12θ2+3θ+9=1n(12θ2+3θ+9)3. θ^3=X¯ Eθ^3=EX¯=E1n∑i=1nXi=1n∑i=1nEXi=1n∑i=1nθ=1n×nθ=θ Bias=θ-Eθ^3=θ-θ=0 varθ^3=VarX¯=Var1n∑i=1nXi=1n2∑i=1nVarXi=1n2∑i=1n1=1n2×n=1n