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November 26th, 2017, 06:06 AM  #1 
Member Joined: Jan 2016 From: Blackpool Posts: 97 Thanks: 2  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. 
November 26th, 2017, 10:28 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,093 Thanks: 1087 
$f_X(x) = \displaystyle \int_x^2 ~(0.5)~dy = 1  \dfrac x 2$ $P[X < 0.5] = \displaystyle \int_0^{0.5}~1\dfrac x 2 ~dx = \dfrac {7}{16}$ 

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density, joint, probability, question2 
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