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Im having a hard time with joint probability when the probability has something to do with X and Y togther (as in parts b and c). Can anyone help with the following question:
If the joint probability density of X and Y is given by:
f(x,y)= 2 for x>0, y>0, x+y<1
= 0 elsewhere
find:
a) P(X≤1/2, Y≤1/2)
b) P(X+Y>2/3)
c) P(X>2Y)
d) an expression for the values of the joint distribution function of X and Y when x>0, y>0, x+y<1
The answers are 1/2, 5/9, and 1/3 with part d) not being in the back of the book but I think I can figure that out once I know what Im doing for part b and c.
For part a, I just took the double integral from 0 to 1 for x and y and came up with 1/2 once it was all evaluated. Not sure about the others and my book isnt too helpful here.
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