The discussion centers on calculating the probability Pr(X≤3/4, Y≤1/2) for jointly continuous random variables X and Y with the joint probability density function (pdf) f(x,y) = 6(1-y) defined for the region 0≤x≤y≤1. The key challenge identified is determining the correct limits of integration for dependent variables. The correct approach involves visualizing the region defined by the joint pdf to establish the appropriate bounds for integration.
PREREQUISITESStudents in statistics or probability courses, educators teaching joint distributions, and anyone looking to deepen their understanding of continuous random variables and their integration.
DotKite said:Homework Statement
Let X and Y be rv's with joint pdf
f(x,y) = 6(1-y) for 0≤x≤y≤1 and 0 elsewhere
find Pr(X≤3/4, Y≤1/2)
Homework Equations
The Attempt at a Solution
Ok I am having trouble with finding the right limits of integration for dependent variables. If we let the inner integral be for x would the limits be 0 to y? Then would y be 1/2 to 1?