Please provide explanation as well Let X and Y be the x and y coordinates, respectively, of a
point selected at random from the four vertices of the unit square. Determine the joint CDF of
the random variables X and Y.
Solution
f(0, 0) = f(0, 1) = f(1, 0) = f(1, 1) = 1/4 (we are randomly selecting points on the vertices of the
unit square).
F(x,y) = 0 on x < 0 U y < 0
F(x,y) = 1/4 on x in [0, 1), y in [0, 1)
F(x ,y) = 1/2 x in [1, inf) and y in [0, 1)
F(x, y) = 1/2 on x in [0, 1) and y in [1, inf)
F(x, y) = 1 on x in [1, inf) and y in [1, inf)
You simply can count points with equal or less x and y than the coordinate and divide by 4.
Thus, for example, if x < 0, no points have x < 0, so the number of points is 0 and F(x, y) = 0.
Please provide explanation as well Let X and Y be the x and .pdf
1. Please provide explanation as well Let X and Y be the x and y coordinates, respectively, of a
point selected at random from the four vertices of the unit square. Determine the joint CDF of
the random variables X and Y.
Solution
f(0, 0) = f(0, 1) = f(1, 0) = f(1, 1) = 1/4 (we are randomly selecting points on the vertices of the
unit square).
F(x,y) = 0 on x < 0 U y < 0
F(x,y) = 1/4 on x in [0, 1), y in [0, 1)
F(x ,y) = 1/2 x in [1, inf) and y in [0, 1)
F(x, y) = 1/2 on x in [0, 1) and y in [1, inf)
F(x, y) = 1 on x in [1, inf) and y in [1, inf)
You simply can count points with equal or less x and y than the coordinate and divide by 4.
Thus, for example, if x < 0, no points have x < 0, so the number of points is 0 and F(x, y) = 0
