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- Let x~ possion(alpha). Show that E[x(x-1)(x-2)....(x-k)]=ak+15. Consider the function f(x) = |x| + 2 at x = 0. Provide a table of inputs and outputs that demonstrate the limitdefinition of the derivative, numericallyIf X is exponentially distributed with parameter λ and Y is uniformly distributed on the interval [a, b], what is the moment generating function of X + 2Y ?
- Let (Nt)t>0 be a Poisson process with parameter λ=2, Find the following: (a) E(X3X4)Two equivalent forms of the Chain Rule for calculating the de-rivative of y = f(g(x)) are presented in this section. State bothforms.Consider a Lorenz curve given by f(x)=x^n for 0≤x≤1 and n≥1. What happens to the Gini index G.I as n→1, and what's the interpretation of that result?