hw9 - Homework Set No. 9 Probability Theory (235A), Fall...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Homework Set No. 9 Probability Theory (235A), Fall 2009 Posted: 11/24/09 Due: Friday, 12/4/09 (Note extended due date!) 1. Compute the characteristic functions for the following distributions. (a) Poisson distribution: X Poisson( ). (b) Geometric distribution: X Geom( p ) (assume a geometric that starts at 1). (c) Uniform distribution: X U [ a,b ], and in particular X [- 1 , 1] which is espe- cially symmetric and useful in applications. (d) Exponential distribution: X Exp( ). (e) Symmetrized exponential: A r.v. Z with density function f Z ( x ) = 1 2 e-| x | . Note that this is the distribution of the exponential distribution after being symmetrized in either of two ways: (i) We showed that if X,Y Exp(1) are independent then X- Y has density 1 2 e-| x | ; (ii) alternatively, it is the distribution of an exponential variable with random sign, namely X where X Exp(1) and is a random sign (same as the coin flip distribution mentioned above) that is independent of...
View Full Document

Page1 / 2

hw9 - Homework Set No. 9 Probability Theory (235A), Fall...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online