{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

160a09_hw3

# 160a09_hw3 - explanation for your result Problem 3 Problem...

This preview shows page 1. Sign up to view the full content.

Pstat160a Winter 2009 Hw #3 Problem 1 Let ( X,Y ) be discrete random variables with joint probability generating function G X,Y ( s 1 ,s 2 ) = exp ± λ 1 ( s 1 - 1) + λ 2 ( s 2 - 1) + γ ( ( s 1 - 1)( s 2 - 1)( s 1 - s 2 ) Show, using a general result from a previous discussion section, that X and Y are both Poisson random variable as well as X + Y . Identify the parameters for each case. Argue that this distribution provides a counter example showing that the converse of the property for sum of independent Poisson random variable shown in class is not true. Problem 2 Use the rejection method to simulate an arbitrary geometric random variable from a a geometric (1/2). For what values values of p would the procedure work? What is the expected number of iteration and give an intuitive
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: explanation for your result. Problem 3 Problem 14, ch 11, only a) b) and c). Problem 4 a) Let X be any random variable, and a ∈ R ﬁxed. Show that cov( X,a ) = 0. b) Let U ∼ U (0 , 1), and let V = 1-U . Show that cov( U,V ) < 0. Problem 5 Download the Matlab program ’rejectgeo.m’ from the class webpage, which implement the algorithm for problem 2 above. Explain it, run it for various values of p , check that indeed only some values of p work and comment. Explain what happens for the p that are not valid. Try also smaller and larger values for C (the bound for the ratio of pdf)....
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online