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November 26th, 2017, 06:06 AM   #1
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Joint probability density question2:

A drinks machine has a random amount Y (in gallons) in
supply at the beginning of a given day and dispenses a random amount X during the day. It is not resupplied during the day and so X ≤ Y . The joint pdf is

f(X,Y)=0.5 0<x<y and 0<y<2

I need to find the probability that less than 0.5gallons are sold.
For this i got -1/2=1/2 but i'm not sure this is correct.
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November 26th, 2017, 10:28 AM   #2
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$f_X(x) = \displaystyle \int_x^2 ~(0.5)~dy = 1 - \dfrac x 2$

$P[X < 0.5] = \displaystyle \int_0^{0.5}~1-\dfrac x 2 ~dx = \dfrac {7}{16}$
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