Draw a picture of the region of positive density d

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Reference no: EM131090574

An ecologist wishes to select a point inside a circu- lar sampling region according to a uniform distribu- tion (in practice this could be done by rst selecting a direction and then a distance from the center in that direction). Let X = the x coordinate of the point0 otherwise

a. What is the probability that the selected point is within R/2 of the center of the circular region? [Hint: Draw a picture of the region of positive den- sity D. Because f (x, y) is constant on D, comput- ing a probability reduces to computing an area.]

b. What is the probability that both X and Y differ from 0 by at most R/2?

c. Answer part (b) for R/ 12 replacing R/2.

d. What is the marginal pdf of X ? Of Y ? Are X and Y independent?

Reference no: EM131090574

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