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).

a

step-by-step explanation:

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.