# Question: A certain random variable has a characteristic function given by Find

A certain random variable has a characteristic function given by

Find the PDF of this random variable.

Find the PDF of this random variable.

## Answer to relevant Questions

Which of the following functions could be the characteristic function of a random variable? See Appendix E, Section 5 for definitions of these functions. (a) f a( ω) = rect( ω ). (b) f b( ω) = tri( ω). (c) f c( ω) = ...A certain random variable has a probability- generating function given by Find the PMF for this random variable. 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. Let X be an Erlang random variable with PDF, Derive a saddle point approximation for the left tail probability, Pr (X< xo). Compare your result with the exact value for 0 ≤ xo < E [X]. Suppose a source sends symbols from a three letter alphabet with X Ɛ {a, b, c} and Pa = 1/ 2, Pb = 1/ 4, Pc = 1/ 4 are the source symbol probabilities. (a) Determine the entropy of this source. (b) Give a source code that ...Post your question