Explaining the rayleigh distribution

Assignment Help Basic Statistics

Reference no: EM131811536

Question: Independence of radial and angular parts. Let X and Y be independent normal (0, σ²) random variables. Let (R, Θ) be (X, Y) in polar coordinates, so X = R cos Θ, Y = R sin Θ.

a) Show that R and Θ are independent, and that Θ has uniform (0, 2π) distribution.

b) Let R and Θ now be arbitrary random variables such that R/σ has the Rayleigh distribution (c1), Θ has uniform (0, 2π) distribution, and R and Θ are independent. Explain why the random variables X = R cos Θ any Y = R sin Θ must be independent normal (0, σ²)

c) Find function h and k such that if U and V are independent uniform (0, 1) random variables, then X = σh(U) cos [k(V)] and Y = σh(U) sin [k(V)] are independent normal (0, σ²). [This gives a means of simulating normal random variables using a computer random number generator. Try generating a random scatter of independent bivariate normally distributed pairs if you have random numbers available, it should look like the scatter.

Reference no: EM131811536

Questions Cloud

Prepare the entry to record the issuance of the warrants : Assume the same facts as part (a), except that the warrants had a fair value of $8. Prepare the entry to record the issuance of the bonds and warrants

Calculate advanced corporations breakeven point : Calculate Advanced Corporation's breakeven point for 20x5 in amount

Replace bar codes with passive rfid tags : What are the factors that you would use to make a decision to replace bar codes with passive RFID tags?

Means of technology-mediated communication : Workers increasingly rely on means of technology-mediated communication in the workplace. Besides e-mail, workers commonly utilize tools

Explaining the rayleigh distribution : Let R and T now be arbitrary random variables such that R/s has the Rayleigh distribution (c1), T has uniform (0, 2p) distribution, and R and T are independent.

Prepare journal entries to record the events and transaction : Prepare journal entries to record the events and transactions. Be sure you indicate the fund in which they would be recorded

Describe yourself to someone that you have never met : Provide a list of 40 words you would use to describe yourself to someone that you have never met. Of those 40, indicate which 10 (ten) are most important

Identify who in the community other than health educators : Develop and name your coalition and identify who in the community, other than health educators, you will want to be part of this coalition.

Compare and contrast legal and ethical issues : Propose alternative response mechanisms that could have more effectively facilitated both civil liberties and domestic security priorities in each context.

User Account

All Pages