3.40 A fast-food restaurant operates both a drivethrough facility and a walk-in facility. On a randomly selected day, let X and Y , respectively, be the proportions of the time that the drive-through and walk-in facilities are in use, and suppose that the joint density function of these random variables is f(x, y) = 2 3 (x + 2y), 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, 0, elsewhere. (a) Find the marginal density of X. (b) Find the marginal density of Y . (c) Find the probability that the drive-through facility is busy less than one-half of the time.

a) Marginal probability of X

b) Marginal probability of Y

c) The probability that the drive-through facility is busy less than one-half of the time is P=0.5.

Step-by-step explanation:

The joint density function of probability is:

a) The marginal density of X is

b) The marginal density of Y is:

c) Probability that the drive-through facility is busy less than one-half of the time. This is P(X<0.5).

point a is the center of the circle that passes through points e, f, and g and the center of the circle that passes through points x, y, and z.

figure c

step-by-step explanation:

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