My Math Forum What is the probability distribution of X+Y?

 Probability and Statistics Basic Probability and Statistics Math Forum

 December 3rd, 2010, 06:14 PM #1 Newbie   Joined: Dec 2010 Posts: 1 Thanks: 0 What is the probability distribution of X+Y? Hi.. I would be grateful if anyone can solve this for me: X1 and X2 follow the distribution: ? x exp(?0.5 ? x2) for x > 0, fX(x) = 0 for x < 0. Given that Y=X1+X2, what is the probability distribution of Y? Thx in advance.
December 4th, 2010, 04:43 PM   #2
Global Moderator

Joined: May 2007

Posts: 6,377
Thanks: 541

Re: What is the probability distribution of X+Y?

Quote:
 Originally Posted by ash_x Hi.. I would be grateful if anyone can solve this for me: X1 and X2 follow the distribution: ? x exp(?0.5 ? x2) for x > 0, fX(x) = 0 for x < 0. Given that Y=X1+X2, what is the probability distribution of Y? Thx in advance.
The general approach to obtain the distribution of the sum of two independent random variables is to take the convolution of the two distribution functions. Alternatively, one can calculate the characteristic functions (Fourier transforms) of the distributions, multiply them and then take the inverse transform of the product.

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post lemon_kaka Advanced Statistics 5 September 23rd, 2013 02:07 PM 450081592 Advanced Statistics 5 November 11th, 2011 03:57 PM Aqil Advanced Statistics 2 April 12th, 2011 02:07 PM tfhawk Algebra 1 July 18th, 2009 07:27 AM RossBrons Advanced Statistics 1 December 28th, 2008 09:35 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top