Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. statistics
  3.       with reference to equations (4.2) and (

      With reference to equations (4.2) and (4.3), let Z1 = U1 and Z2 = ?U2 be...

80.2K

Verified Solution

Question

Statistics

      With reference to equations (4.2)and (4.3), let Z1 = U1 and Z2 =?U2 be independent, standard normal variables.Consider the polar coordinates of the point (Z1,Z2), that is,

A2 = Z2 + Z2

and   ? =tan?1(Z2/Z1).

1         2

(a)    Find the joint density of A2 and?, and from the result, conclude that A2 and? are independent random variables, where A2 is achi-

squared random variable with 2 df, and ? is uniformlydistributed on (??, ?).

(b)    Going in reverse from polar coordinates torectangular coordinates, suppose we assume that A2 and? are independent random variables, where A2 ischi-squared with 2 df, and ? is uniformly distributed

on (??, ?). With Z1 =A cos(?) and Z2 = Asin(?), where A is the

positive square root of A2, show that Z1 andZ2 are independent,

standard normal random variables.

Answer & Explanation Solved by verified expert
3.8 Ratings (758 Votes)
    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Chemistry
1.2K views

C: CaCO3 (s) ----> CaO (s) + CO2 (g) delta H= +178 kJ/mol D: PCl3 (g) +...

Biology
1.2K views

Overall, when we consider the number of animal families over time, the trend since the...

Biology
1.2K views

In some plants a fruit is composed of the ovary and other plant parts 1...

Geometry
1.2K views

Use the Pythagorean theorem to determin e triangle and c determine the area of the

Basic Math
1.2K views

The table below cross classifies the price of 486 stocks in a particular stock exchange,...

Accounting
1.2K views

1. An employee has gross pensionable/taxable income of $3,000.00 per month....

Accounting
1.2K views

Parenting Comma Company makes and sells widgets. The company is in the process of preparing...

Accounting
1.2K views

urgent !! please help by showing work on e-notes/ notebook NOT excel or other...

Accounting
1.2K views

How would these items be classified in a cash flow statement prepared for a wholesale...

Accounting
1.2K views

Information about the July work in process (WIP) inventory follows. Use this information with that...

Accounting
1.2K views

what is the correct answer for number 6 ans 7? Selected...

Finance
1.2K views

Data on Party Palace Co. for the most recent year are shown below, along with...