This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: , 0 x 4, f ( x ) = 0, otherwise. a) What must the value of k be so that f ( x ) is a probability density function? b) Find the cumulative distribution function of X, F X ( x ) = P ( X x ). c) Find the probability P ( 1 X 2 ). d) Find the median of the distribution of X. That is, find m such that P ( X m ) = P ( X m ) = 1 / 2 . e) Find the 30th percentile of the distribution of X. That is, find a such that P ( X a ) = 0.30. f) Find X = E ( X ). g) Find X = SD ( X ). 2. Let X be a continuous random variable with the cumulative distribution function F ( x ) = 0, x < 0, F ( x ) = 8 3 x , 0 x 2, F ( x ) = 1 2 1 x , x > 2. a) Find the probability density function f ( x ). b) Find the probability P ( 1 X 4 ). c) Find X = E ( X ). d) Find X = SD ( X )....
View
Full
Document
This note was uploaded on 02/24/2011 for the course STAT 400 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.
 Spring '08
 Kim
 Probability

Click to edit the document details