 My Math Forum Standard Deviation of Squared Gaussian Distribution

 March 11th, 2015, 11:01 PM #1 Newbie   Joined: Mar 2015 From: USA Posts: 1 Thanks: 0 Standard Deviation of Squared Gaussian Distribution Hello Everyone, I have a quick question. Assuming we have a random variable described by a Gaussian probability density function: f(x) = 1/((2*pi)^0.5*s)*exp(x^2/(2s^2)) If a new random variable is defined as: y = x*x. What would be a probability density function describing it and what would be its standard deviation? Thank you, AeroX March 12th, 2015, 02:00 PM #2 Global Moderator   Joined: May 2007 Posts: 6,768 Thanks: 699 Let $\displaystyle Y=X^2$ where X is N(0,s), call it f(x). The distribution function for Y (P(Y
 March 12th, 2015, 02:59 PM #3 Global Moderator   Joined: May 2007 Posts: 6,768 Thanks: 699 If you don't need the density function, the mean and standard deviation can be computed directly: $\displaystyle E(Y)=E(X^2)=s^2,\ E(Y^2)=E(X^4)=3s^4$ Therefore the standard deviation of Y is $\displaystyle \sqrt 2 s^2$ Tags deviation, distribution, gaussian, squared, standard Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post EvanJ Advanced Statistics 4 December 23rd, 2013 08:35 AM questioner1 Algebra 7 July 9th, 2012 04:28 PM youngstor Advanced Statistics 5 June 18th, 2012 01:35 PM bilano99 Algebra 3 March 21st, 2012 10:20 PM Axel Algebra 2 April 28th, 2011 03:25 AM

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