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 given below. f(x, y) = 1/TR2 X2 + Y2 + R2
otherwise
A) What is the probability that the selected poi of the center of the circular region?
B) What is the probability that both X and Y differ from 0 by at most?
C) What is the probability that both X and Y differ from O by at most?