
#1
Nov1911, 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 = K^{2} I get: f_{X}(x) = √(2/π) e^{x2/2} and f_{Y}(y) = 1/√(2*π) 1/√y e^{y2/2} 



#2
Nov1911, 11:00 PM

P: 376

it's correct




#3
Nov2011, 12:27 AM

P: 4,570

For the Y random variable, it is definitely a chisquared distribution with 1 degree of freedom.




#4
Nov2011, 12:58 AM

P: 376

Please check my work: Probability Theory 



#5
Nov2011, 01:20 AM

P: 4,570

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. 



#6
Nov2011, 01:35 PM

P: 376

Thanks Chiro



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