A random variable has probability density in a given family. The family (or the distribution) is said to be stable before additions if for each pair of positive constants a and a1, there is another positive constant such that S(a12) * S(a2a) = S(ax) where denotes convolution. The definition is due to Levy. Show that 1) A Gaussian family f(x)= - 2) A Cauchy family fe(x) = %3D %3D are stables.

A random variable has probability density in a given family. The family (or the distribution) is said to be stable before additions if for each pair of positive constants a and a1, there is another positive constant such that S(a12) * S(a2a) = S(ax) where denotes convolution. The definition is due to Levy. Show that 1) A Gaussian family f(x)= - 2) A Cauchy family fe(x) = %3D %3D are stables.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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