Introduction

Please complete the following tasks regarding the data in R. Please generate a solution

document in R markdown and upload the .Rmd document and a rendered .doc, .docx, or

.pdf document. Your work should be based on the data's being in the same folder as the

.Rmd file. Please turn in your work on Canvas. Your solution document should have your

answers to the questions and should display the requested plots. Each part is worth 10

points.

These questions were rendered in R markdown through RStudio

(https://www.rstudio.com/wp-content/uploads/2015/02/rmarkdown-cheatsheet.pdf,

http://rmarkdown.rstudio.com).

1

Recall that if Z is a random variable with the standard Normal distribution, then the

distribution of Z² (the result of applying the function f(z) = z² to the outcomes of Z) has a

x distribution. If Z₁, Z₂,...Z, are independent random variables with the standard Normal

distribution, then the distribution of ₁Z² is a x² distribution.

Also, recall the fact from the week 5 slides that if X and Y are random variables and Y=

g(x) then Ex [g(x)] = Ey[Y].

1.a

(5 points)

Please compute the expected value of x₁, the x² distribution with 1 degree of freedom.

1.b

(5 points)

Based on your answer to 1.a, please compute the expected value of x2, the x² distribution

with n degrees of freedom.