Guest SNJERIN Posted January 29, 2016 Report Share Posted January 29, 2016 (edited) Hello. I would appreciate it if someone could help me with proving that Var(X)=1. Determining E(x) is straight forward but the integral for Var(X) causes me trouble, because it can't be solved using integration by part. Edited January 29, 2016 by Haitham Wahid Reply Link to post Share on other sites More sharing options...
eross Posted January 29, 2016 Report Share Posted January 29, 2016 two things: is it a paper 1 or a paper 2 question? and what did you get for E(x) ? I'll try to solve it and see where I get Reply Link to post Share on other sites More sharing options...
Guest SNJERIN Posted January 29, 2016 Report Share Posted January 29, 2016 For E(x) I got zero, which is the correct value. I am not sure whether it is a paper 1 or 2 question since I got it from my math book. However, since "prove" is in the question, I doubt it can be solved using GDC. Reply Link to post Share on other sites More sharing options...
eross Posted January 29, 2016 Report Share Posted January 29, 2016 For E(x) I got zero, which is the correct value. I am not sure whether it is a paper 1 or 2 question since I got it from my math book. However, since "prove" is in the question, I doubt it can be solved using GDC. okay, I got 0 as well, but I'm using my GDC. for the Var(x), I'm not getting 1 though. From the formula booklet, Var(x)= [integral from -infinity to +infinity of] x2 f(x) dx - u2 since u= 0, Var(x) is just the integral right? So I TRIED graphing x2 f(x) (which is x2/2pi * e^ -x2/2 ) and getting the integral from the calculator, but I get 0.399 instead of 1. I'm not sure where my method is wrong, but if you (or anyone else) notices, let me know how were you trying to solve it? Reply Link to post Share on other sites More sharing options...
kw0573 Posted January 29, 2016 Report Share Posted January 29, 2016 (edited) Here is the proof on wikibooks.Question 7 is the standardized normal distribution (mu = 0, sigma = 1), wikibooks proves the general case.https://en.wikibooks.org/wiki/Statistics/Distributions/Normal_(Gaussian)#VarianceIt also makes use of the (not well known) fact thatYou just have to know this to cancel out the denominator in f(x). Here is another proof that does not use L'Hopital's Rule http://www.statlect.com/ucdnrm1.htm. Although you have personally proved that the E(X) is 0. In the link, under the standardized normal distribution, expand the proof for the variance. Edited January 29, 2016 by kw0573 1 Reply Link to post Share on other sites More sharing options...
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