A privately owned liquor store operates both a drive-in 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- in and walk-in facilities are in use, and suppose that the joint density function of these variables is; f(x, y) = 0, (x + 2y), 0 < x < 1,0 sys1, elsewhere. A. Find the marginal density of X. B. Find the marginal density of Y. C. Find the probability that the drive-in facility is busy less than one-half of the time.

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Probability Distribution

A privately owned liquor store operates both a drive-in 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-
in and walk-in facilities are in use, and suppose that the joint density function of these
variables is;
f(x, y) = }3 (x + 2y),0<x< 1,0 < y s 1,
elsewhere.
0,
A. Find the marginal density of X.
B. Find the marginal density of Y.
C. Find the probability that the drive-in facility is busy less than one-half of the time.
Transcribed Image Text:A privately owned liquor store operates both a drive-in 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- in and walk-in facilities are in use, and suppose that the joint density function of these variables is; f(x, y) = }3 (x + 2y),0<x< 1,0 < y s 1, elsewhere. 0, A. Find the marginal density of X. B. Find the marginal density of Y. C. Find the probability that the drive-in facility is busy less than one-half of the time.
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