Let X1, X2, ... , X18 be a random sample of size 18 from a chi-square distribution with

Chapter 5, Problem 5.6-5

(choose chapter or problem)

Get Unlimited Answers
QUESTION:

Let \(X_{1}, X_{2}, \ldots, X_{18}\) be a random sample of size 18 from a chi-square distribution with r = 1. Recall that \(\mu=1\) and \(\sigma^{2}=2\).

(a) How is \(Y=\sum_{i=1}^{18}\ X_i\) distributed?

(b) Using the result of part (a), we see from Table IV in Appendix B that

\(P(Y \leq 9.390)=0.05\) and \(P(Y \leq 34.80)=0.99\).

Compare these two probabilities with the approximations found with the use of the central limit theorem.

Questions & Answers


(1 Reviews)

QUESTION:

Let \(X_{1}, X_{2}, \ldots, X_{18}\) be a random sample of size 18 from a chi-square distribution with r = 1. Recall that \(\mu=1\) and \(\sigma^{2}=2\).

(a) How is \(Y=\sum_{i=1}^{18}\ X_i\) distributed?

(b) Using the result of part (a), we see from Table IV in Appendix B that

\(P(Y \leq 9.390)=0.05\) and \(P(Y \leq 34.80)=0.99\).

Compare these two probabilities with the approximations found with the use of the central limit theorem.

ANSWER:

Step 1

Given that,

\(n = 18\)

\({X_i} \sim {\chi ^2}\left( 1 \right)\)

\(\mu  = 1\)

\({\sigma ^2} = 2\)

Add to cart

Reviews

Review this written solution for 630465) viewed: 574 isbn: 9780321923271 | Probability And Statistical Inference - 9 Edition - Chapter 5.6 - Problem 5.6-5

Thank you for your recent purchase on StudySoup. We invite you to provide a review below, and help us create a better product.

Textbook: Probability and Statistical Inference

Click to rate

Write a review below (optional):

Submit Review
×

Thanks for your review!

Think of all the students you've helped. Nice job!


Study Tools You Might Need

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back