My Math Forum  

Go Back   My Math Forum > High School Math Forum > Probability and Statistics

Probability and Statistics Basic Probability and Statistics Math Forum

Thanks Tree1Thanks
  • 1 Post By romsek
LinkBack Thread Tools Display Modes
November 26th, 2017, 07:06 AM   #1
Senior Member
Joined: Jan 2016
From: Blackpool

Posts: 100
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.
Jaket1 is offline  
November 26th, 2017, 11:28 AM   #2
Senior Member
romsek's Avatar
Joined: Sep 2015
From: USA

Posts: 2,197
Thanks: 1152

$f_X(x) = \displaystyle \int_x^2 ~(0.5)~dy = 1 - \dfrac x 2$

$P[X < 0.5] = \displaystyle \int_0^{0.5}~1-\dfrac x 2 ~dx = \dfrac {7}{16}$
Thanks from Jaket1
romsek is offline  

  My Math Forum > High School Math Forum > Probability and Statistics

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 11:13 AM
Joint Probability Density Function of a Sample of A Normal Distribution IndependentThinker Advanced Statistics 1 February 27th, 2015 03:01 PM
How to form Joint Probability Density from two Gaussian Distributions? Giri Advanced Statistics 0 June 30th, 2014 04:04 PM
Joint probability density function Idiot Advanced Statistics 3 October 5th, 2012 04:11 AM
Joint probability density function, probability token22 Advanced Statistics 2 April 26th, 2012 04:28 PM

Copyright © 2018 My Math Forum. All rights reserved.