Let X has the pdf f (x) = 3x², 0 < x < 1, zero elsewhere. Consider a random rectangle whose sides are X and (1-X). Determine the expected value of the area of the rectangle. Find the mean and variance, if they exist, of each of the following distributions. (a) p(x) = 3!/x!(3−x)! * (1/2)³, x = 0, 1, 2, 3, zero elsewhere. (b) f (x) = 6x(1 − x), 0 < x <
Let X has the pdf f (x) = 3x², 0 < x < 1, zero elsewhere. Consider a random rectangle whose sides are X and (1-X). Determine the expected value of the area of the rectangle.
Find the mean and variance, if they exist, of each of the following distributions.
(a) p(x) = 3!/x!(3−x)! * (1/2)² x = 0, 1, 2, 3, zero elsewhere.
(b) f (x) = 6x(1 − x), 0 < x < 1, zero elsewhere.
(c) f (x) = 2/x^3 , 1 < x < [infinity], zero elsewhere.
