Ex4 - X 2 Q4.If two r.v.’s X and Y are independent and...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT 1306: INTRODUCTORY STATISTICS Sem 1 2008/2009 EXAMPLE CLASS 4 Q1. Cast a die a number of independent times until a six appears on the upside of the die. (a) What is the distribution? (b) Find the p.d.f. (c) Show that y =1 f ( y ) = 1 (d) Determine P ( Y = 1 , 3 , 5 , 7 ,...... ) (e) Find the distribution function F ( Y ) = P ( Y y ) 1
Background image of page 1

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

View Full DocumentRight Arrow Icon
Q2. Let X be a discrete random variable. (a) What is the moment generating function (m.g.f.) of X ? (b) Differentiate the m.g.f. (with respect to t) and set t=0. Show that this technique gives the moments of X. Q3. If a r.v. X has the m.g.f. M X ( t ) = 1 2 e t + 1 3 e 2 t + 1 6 e 3 t , then find the probability function of
Background image of page 2
Background image of page 3

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

View Full DocumentRight Arrow Icon
Background image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: X . 2 Q4.If two r.v.’s X and Y are independent and have probabilities given by P ( X =-1) = 1 4 , P ( X = 0) = 1 2 , P ( X = 2) = 1 4 , and P ( Y = 3) = 1 3 , P ( Y = 4) = 2 3 , (i) Find the m.g.f.s of X and Y . (ii) Find the m.g.f. of Z = X + Y , and use this to derive its probability function. 3 Q5. Suppose that the m.g.f. of X is M X ( t ) = e t / 2 1-e t / 2 . Find the probability function of X . Q6. Let the moments of X be defined by: E ( X r ) = 0 . 8 for r = 1 , 2 , 3 ,...... (a) Find the moment-generating function of X . (b) What is the p.m.f.? (c) What is the distribution? 4...
View Full Document

This note was uploaded on 09/06/2010 for the course STAT STAT1306 taught by Professor Prof during the Fall '08 term at HKU.

Page1 / 4

Ex4 - X 2 Q4.If two r.v.’s X and Y are independent and...

This preview shows document pages 1 - 4. Sign up to view the full document.

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