
Advanced Statistics Advanced Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
October 19th, 2015, 08:59 AM  #1 
Member Joined: Jan 2012 Posts: 57 Thanks: 0  function of random variable
suppose X is uniformly distributed over [1,3] and $\displaystyle Y=X^2$ Find the CDF $\displaystyle F_{Y}(y)$? since X is unoformly distrbuted $\displaystyle f_{X}(x)=\frac{1}{4} $ for [1,3] otherwise 0. $\displaystyle F_{Y}(y)=P[X^{2}\leqslant y]=P[\sqrt{y} \leqslant X\leqslant \sqrt{y} ]=\int_{\sqrt{y}}^{\sqrt{y}}f_{X}(x)dx $ the calculation of the integral depends on the value of y I don't know how to deal the rest of the problem for example what is the value of $\displaystyle F_{Y}(y)$ for $\displaystyle 0\leq y\leq 1$ or $\displaystyle 1\leq y\leq 9$ thanks Last edited by mhhojati; October 19th, 2015 at 09:11 AM. 
October 19th, 2015, 01:58 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,338 Thanks: 532 
You need to separate the integral into 2 cases. For y < 1, use the integral as is. For y > 1, the lower limit should be 1.

October 19th, 2015, 07:56 PM  #3 
Member Joined: Jan 2012 Posts: 57 Thanks: 0 
can you please tell me the general ideas for solving such problems or introduce some good books I'm stuck with such problems

October 20th, 2015, 05:46 PM  #4 
Global Moderator Joined: May 2007 Posts: 6,338 Thanks: 532 
I don't have any particular recommendation. However, your approach was correct, except for not taking care of the lower limit of x (1) when applicable.


Tags 
function, random, variable 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Construction of a random variable for a given cdf F  smieci  Advanced Statistics  0  April 10th, 2014 04:01 PM 
random variable!  lawochekel  Algebra  1  April 19th, 2012 12:39 PM 
distribution of a function of a random variable problem  frankpupu  Advanced Statistics  2  March 1st, 2012 03:45 AM 
can a random variable donimant  Jill  Advanced Statistics  0  July 22nd, 2010 07:39 AM 
function of random variable  benjaminmar8  Advanced Statistics  1  April 10th, 2008 07:14 AM 