chap2 prob 13 ans

chap2 prob 13 ans - School of Mathematics MATH1715:...

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: School of Mathematics MATH1715: Introduction to Probability Session 2008/2009 Solutions to Homework III H3.1. (a) X x p X ( x ) = 0 . 1 + 0 . 2 + 0 . 15 + 0 . 2 + 0 . 1 + 0 . 15 + 0 . 05 + 0 . 05 = 1 . (b) • P (1 ≤ X ≤ 4) = p X (1) + p X (2) + p X (3) = 0 . 2 + 0 . 1 + 0 . 15 = 0 . 45 . • P ( X is negative ) = p X (- 3) + p X (- 1) = 0 . 1 + 0 . 2 = 0 . 3 . • P ( X ≥ 3 | X > 0) = P ( X ≥ 3 , X > 0) P ( X > 0) = P ( X ≥ 3) P ( X > 0) = = . 15 + 0 . 05 + 0 . 05 . 2 + 0 . 1 + 0 . 15 + 0 . 05 + 0 . 05 = . 25 . 55 = 5 11 . (c) y 1 4 9 25 64 p Y ( y ) . 15 . 4 . 1 . 25 . 05 . 05 (d) To calculate the mean and variance we need to extend the probability distribution tables with two extra rows: x- 3- 1 1 2 3 5 8 p X ( x ) . 1 . 2 . 15 . 2 . 1 . 15 . 05 . 05 xp X ( x )- . 3- . 2 . 2 . 2 . 45 . 25 . 4 x 2 p X ( x ) . 90 . 20 . 2 . 4 1 . 35 1 . 25 3 . 2 y 1 4 9 25 64 p Y ( y ) . 15 . 4 . 1 . 25 . 05 . 05 yp Y ( y ) . 4 . 4 2 . 25 1 . 25 3 . 2 y 2 p Y ( y ) . 4 1 . 6 20 . 25 21 . 25 204...
View Full Document

This note was uploaded on 09/24/2009 for the course IE 221 taught by Professor Georgewilson during the Spring '08 term at Lehigh University .

Page1 / 3

chap2 prob 13 ans - School of Mathematics MATH1715:...

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