# Question

Prove Jensen’s inequality, which states that for any convex function g (x) and any random variable X,

E [ g( X)] ≥ g ( E [ X]).

E [ g( X)] ≥ g ( E [ X]).

## Answer to relevant Questions

Find an expression for the m th moment of an Erlang random variable whose PDF is given by for some positive integer n and positive constant b. Suppose X is a random variable whose n th moment is gn , n = 1,2, 3.… In terms of the gn, find an expression for the m th moment of the random variable Y= aX+ b for constants a and b . Let cn be the n th central moment of a random variable and µ n be its n th moment. Find a relationship between cn and µk, k = 0, 1, 2… Find the mean of the random variables described by each of the following cumulative distribution functions: (a) (b) (c) (d) Consider a Gaussian random variable, X , with mean µ and variance σ2. The random variable is transformed by the device whose input– output relationship is shown in the accompanying figure. Find and sketch the PDF of the ...Post your question

0