
Probability and Statistics Basic Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
November 26th, 2017, 06:06 AM  #1 
Member Joined: Jan 2016 From: Blackpool Posts: 95 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: 1,975 Thanks: 1026 
$f_X(x) = \displaystyle \int_x^2 ~(0.5)~dy = 1  \dfrac x 2$ $P[X < 0.5] = \displaystyle \int_0^{0.5}~1\dfrac x 2 ~dx = \dfrac {7}{16}$ 

Tags 
density, joint, probability, question2 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Joint probability density question:  Jaket1  Probability and Statistics  2  November 26th, 2017 10:13 AM 
Joint Probability Density Function of a Sample of A Normal Distribution  IndependentThinker  Advanced Statistics  1  February 27th, 2015 02:01 PM 
How to form Joint Probability Density from two Gaussian Distributions?  Giri  Advanced Statistics  0  June 30th, 2014 03:04 PM 
Joint probability density function  Idiot  Advanced Statistics  3  October 5th, 2012 03:11 AM 
Joint probability density function, probability  token22  Advanced Statistics  2  April 26th, 2012 03:28 PM 