
Advanced Statistics Advanced Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
February 2nd, 2016, 12:45 PM  #1 
Newbie Joined: Feb 2016 From: Michigan Posts: 2 Thanks: 0  Random variable with continuous distribution
Hello, I'm stuck with following problem: Random variable X with the continuous distribution for some arbitrary constant a > 0: $\displaystyle p(x) = 3/4a³(a²  x²)$ if x < a otherwise 0 i. Draw the distribution ii. Show that p(x) is a valid distribution Some hints how to get started with the problem would be appreciated! 
February 2nd, 2016, 02:49 PM  #2 
Math Team Joined: Nov 2014 From: Australia Posts: 689 Thanks: 244 
Can you clarify $p(x)$? Is it $\dfrac{3}{4a^2(a^2  x^2)}$, $\dfrac{3}{4a^2}(a^2  x^2)$, $\dfrac{3}{4}a^2(a^2  x^2)$? A small latex tip; If you want to make your exponents more visible, use ^n. For example, the code a^n will give $a^n$. 
February 2nd, 2016, 04:41 PM  #3  
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics  Quote:
For ii), you have to show that the area under the curve = 1, i.e. integrate p(x) from a to a.  
February 2nd, 2016, 09:25 PM  #4 
Newbie Joined: Feb 2016 From: Michigan Posts: 2 Thanks: 0  p(x) is: $\displaystyle p(x) = \frac{3}{4a^{3}}(a^2x^2)$ 

Tags 
continuous, distribution, random, variable 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Continuous random variable  lstevens  Probability and Statistics  1  October 19th, 2015 01:39 PM 
Continuous random variable  tayyeb  Probability and Statistics  6  March 19th, 2015 11:50 AM 
probability at a point for a continuous random variable  rsashwinkumar  Advanced Statistics  3  January 7th, 2013 03:25 PM 
Geometry & Continuous Random Variable Distribution  fin0c  Advanced Statistics  1  January 23rd, 2011 10:43 PM 
Help! Distribution of random variable  alfangio  Advanced Statistics  1  March 17th, 2009 01:46 PM 