Hw5Sol - SIEO 3600 (IEOR Majors) Solution to Assignment #5...

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: SIEO 3600 (IEOR Majors) Solution to Assignment #5 Introduction to Probability and Statistics February 24, 2010 Solution to Assignment #5 1. X is a continuous random variable with probability density function f X ( x ) = 1 / 2 , if 2 < x < 4; , otherwise . (a) Compute P ( X < 3). (b) Compute R xf ( x ) dx and R x 2 f ( x ) dx . (c) Show that the cumulative distribution function F X ( x ) = , if x 2; ( x- 2) / 2 , if 2 < x < 4; 1 , if x 4 . (d) Let F X ( x ) 1- F X ( x ), show that F X ( x ) = 1 , if x 2; (4- x ) / 2 , if 2 < x < 4; , if x 4 . (e) Graph both F X ( x ) and F X ( x ). (f) Show that R xf ( x ) dx = R F ( x ) dx . Solution: (a) P [ X < 3] = R 3 2 1 2 dx = 1 2 . (b) The mean is E [ X ] = R 4 2 x 2 dx = 3, The second moment is E [ X 2 ] = R 4 2 x 2 2 dx = 28 3 . (c) If x < 2 we never make it to the interval [2 , 4] where f lives and thus the integral or, the probability (the total area is always 1!) under the graph is zero. If x [2 , 4] we have F ( x ) = R x- f ( t ) dt = R x 2 1 2 dt = x- 2 2 . Finally, if x > 2 we have F ( x ) = R x- f ( t ) dt = R 4 2 1 2 dt = 1....
View Full Document

Page1 / 4

Hw5Sol - SIEO 3600 (IEOR Majors) Solution to Assignment #5...

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