Normal Distribution

hianitya · January 8th, 2007, 5:48 pm

If X is normally distributed with means 0 and standard deviation = 1, then I understand that E[X] =0.Can someone please explain why E[X^2] =1?Thanks,

hianitya · January 8th, 2007, 8:35 pm

Thanks a lot.I guess another related question is...If I want to express say returns as a function of a random variable and knowing that returns are normally distributed, why is Ri = mean + standard deviation × φ.why not anything something else like Ri = mean + ((standard deviation)^2) × φ.May be something really primary, but I do not know where to source this. Thanks,

bhutes · January 9th, 2007, 10:53 am

QuoteOriginally posted by: hianityaThanks a lot.I guess another related question is...If I want to express say returns as a function of a random variable and knowing that returns are normally distributed, why is Ri = mean + standard deviation ~ Ó.why not anything something else like Ri = mean + ((standard deviation)^2) ~ Ó.May be something really primary, but I do not know where to source this. Thanks,

mensa0 · January 14th, 2007, 5:58 am

hianitya - Learning opportunity! In Excel, generate a random sample of, say, 50 observations. Compute the mean, stdev and variance of these data. Now multiply each observation by a constant. Compute the mean, stdev and variance of these data. Compare!Now after you've seen this for yourself, consult any elementary statistics text for the mathematical derivation of what you've observed.Mike