
Advanced Statistics Advanced Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
April 26th, 2017, 10:25 AM  #1 
Member Joined: Apr 2017 From: PA Posts: 45 Thanks: 0  Finding a cdf
2 Choose a number U from the interval [0, 1] with uniform distribution. Find the cumulative distribution and density for the random variables (a) Y = 1/(U + 1). Attempt: I used a theorem F (Y)=P (Y<y) to get P ( 1/(U+1) is less than or equal to y), then I got P ( 1(1/y) is less than or equal to U is less than or equal to (1/y) 1), so Later I came up with a CDF of F (y)=( 1/y)  1 on [ 1/2,1 ] since it has to be uniform on [0,1]. However the cdf was 2(1/y). How did they get that CDf? 
April 26th, 2017, 12:36 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 1,859 Thanks: 966 
$Y \sim \dfrac{1}{U+1}$ $\begin{align*} &\phantom{=}F_Y(y)=P[Y<y] \\ \\ &=P[\dfrac{1}{U+1}<y] \\ \\ &=P[\dfrac 1 y  1 < U] \\ \\ &=1  Pr[U < \dfrac 1 y  1] \\ \\ &=1  \left(\dfrac 1 y  1\right),~y \in \left[\dfrac 1 2,~1\right] \\ &=2\dfrac 1 y,~y \in \left[\dfrac 1 2,~1\right] \end{align*}$ 

Tags 
cdf, finding 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Finding a PDF from a CDF  KaiL  Probability and Statistics  1  March 20th, 2016 11:46 AM 
Finding the max.  Tamer Ghareeb  Calculus  1  August 26th, 2015 01:37 PM 
Finding x  alifeee  Algebra  8  November 22nd, 2014 05:47 PM 
Finding max/min  Lucida  Calculus  5  January 20th, 2013 04:29 PM 
finding 'x'  mielke  Algebra  8  June 2nd, 2011 06:21 PM 