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If the joint probability distribution of X and Y is given by:

A privately owned liquor store operates both drive-in facility and walk-in facility. On randomly selected day, let X and Y, respectively, be the proportions of time that the drive-in and walk-in facilities are in employ, and assume 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 out the marginal density of X.

b) Find out the marginal density of Y.  

c) Find out the probability that the drive-in facility is busy less than one-half of the time.

Statistics and Probability, Statistics

  • Category:- Statistics and Probability
  • Reference No.:- M920366

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