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An ecologist wishes to select a point inside a circular sampling region according to a uniform distribution

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An ecologist wishes to select a point inside a circular sampling region according to a uniform distribution (in practice this could be done by first selecting a direction and then a distance from the center in that direction). Let X = the x coordinate of the point selected and Y = the y coordinate of the point selected. If the circle is centered at (0, 0) and has radius R, then the joint pdf of X and Y is
An ecologist wishes to select a point inside a circular

a. What is the probability that the selected point is within R/2 of the center of the circular region?
b. What is the probability that both X and Y differ from 0 by at most R/2?
c. Answer part (b) for R/ˆš2 replacing R/2.
d. What is the marginal pdf of X? Of Y? Are X and Y independent?

Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...
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/L»-倖 nR 0 .athySF f(x, y)= otherwise

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a Let A denote the disk of radius R2 Then That sinc...View the full answer


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Probability And Statistics For Engineering And The Sciences

Probability And Statistics For Engineering And The Sciences

ISBN: 9781305251809

9th Edition

Authors: Jay L. Devore

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