Generating Functions, Taylor Series, Taylor Theorem, Central Limit Theorem, Deep Dives.
the Taylor series expansion of e to the power tX evaluated at t = 0: Taylor series expansion of e to the power tX at t = 0 (Image by Author) Let’s apply the Expectation operator on both sides of the above equation: (Image by Author) By linearity (and scaling) rule of expectation: E(aX + bY) = aE(X)