Q12Single correct3 Marks4 Aug 2024Let X1X_1X1 and X2X_2X2 be i.i.d., where XXX has PMF P(X=0)=0.2P(X=0)=0.2P(X=0)=0.2, P(X=1)=0.4P(X=1)=0.4P(X=1)=0.4, P(X=2)=0.4P(X=2)=0.4P(X=2)=0.4. Define Y=X1+X2Y=X_1+X_2Y=X1+X2. Find the MGF of YYY.AMY(λ)=(0.2+0.4eλ+0.4e2λ)2M_Y(\lambda)=(0.2+0.4e^\lambda+0.4e^{2\lambda})^2MY(λ)=(0.2+0.4eλ+0.4e2λ)2BMY(λ)=0.2+0.4eλ+0.4e2λM_Y(\lambda)=0.2+0.4e^\lambda+0.4e^{2\lambda}MY(λ)=0.2+0.4eλ+0.4e2λCMY(λ)=(0.4eλ+0.4e2λ)2M_Y(\lambda)=(0.4e^\lambda+0.4e^{2\lambda})^2MY(λ)=(0.4eλ+0.4e2λ)2DMY(λ)=0.2+0.4e2λM_Y(\lambda)=0.2+0.4e^{2\lambda}MY(λ)=0.2+0.4e2λ
