Please check my work: Probability Theory


by Bachelier
Tags: check, probability, theory, work
Bachelier
Bachelier is offline
#1
Nov19-11, 08:37 PM
P: 376
Let K be a standard normal random variable. Find the densities of each of the following random variables:

X= |K|

Y = K2

I get:

fX(x) = √(2/π) e-x2/2

and

fY(y) = 1/√(2*π) 1/√y e-y2/2
Phys.Org News Partner Science news on Phys.org
Simplicity is key to co-operative robots
Chemical vapor deposition used to grow atomic layer materials on top of each other
Earliest ancestor of land herbivores discovered
Bachelier
Bachelier is offline
#2
Nov19-11, 11:00 PM
P: 376
it's correct
chiro
chiro is offline
#3
Nov20-11, 12:27 AM
P: 4,570
For the Y random variable, it is definitely a chi-squared distribution with 1 degree of freedom.

Bachelier
Bachelier is offline
#4
Nov20-11, 12:58 AM
P: 376

Please check my work: Probability Theory


Quote Quote by chiro View Post
For the Y random variable, it is definitely a chi-squared distribution with 1 degree of freedom.
We skipped the Chi-Squared dsn. I think I should read about it on Wikipedia. Where is it mostly used in?
chiro
chiro is offline
#5
Nov20-11, 01:20 AM
P: 4,570
Quote Quote by Bachelier View Post
We skipped the Chi-Squared dsn. I think I should read about it on Wikipedia. Where is it mostly used in?
Chi-squared distributions are used in a variety of cases.

One application is what is called goodness of fit. This is used to test how an observed set of frequencies are fitted to some expected set of frequencies.

Another application is for representing the sampling distribution of the ratio of the sample variance to the true variance. Given your degrees of freedom, you get a distribution that allows you to calculate a confidence interval for the ratio of sample variance to true variance, which effectively allows you to get an interval for your variance since you can calculate your sample variance from your data.

These uses are for classical frequentist statistics where these rely on asymptotic results.
Bachelier
Bachelier is offline
#6
Nov20-11, 01:35 PM
P: 376
Thanks Chiro


Register to reply

Related Discussions
Simple Probability Check Calculus & Beyond Homework 3
[probability theory] simple question about conditional probability Precalculus Mathematics Homework 1
Work input/output, efficient probelm, just need someone to check my work :) Introductory Physics Homework 1
Probability HW (check my work & help) Introductory Physics Homework 1