# Question: A random variable has a moment generating function given by a

A random variable has a moment- generating function given by

(a) Find the PDF of the random variable.

(b) Use the moment- generating function to find an expression for the k th moment of the random variable.

(a) Find the PDF of the random variable.

(b) Use the moment- generating function to find an expression for the k th moment of the random variable.

## Answer to relevant Questions

Consider a moment- generating function of the general form For constants a, b, and c. Find constraints that the constants a, b, and c must satisfy so that MX (u) is the MGF of a valid random variable. Suppose we are interested in finding the left tail probability for a random variable, X. That is, we want to find Pr (X≤ xo). Rederive an expression for the Chernoff bound for the left tail probability. The received voltage in a 75 Ω antenna of a wireless communication system is modeled as a Rayleigh random variable, What does the value of the parameter σ need to be for the received power to be 10µW ? Consider an N - letter source with probabilities, Pi, i = 1, 2, 3… N. The entropy of the source is given by Prove that the discrete distribution that maximizes the entropy is a uniform distribution. Hint: You need to ...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.Post your question