- #1
esvee
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Homework Statement
The r.v (X,Y) is distributed uniformly in the triangle with vertices (0,0), (1,0), (1,-1).
claim (a): The variable (X^2, Y^2) is distributed uniformly in the region {(x,y): 0 <= x <= 1, 0 <= y <= x^2}.
Homework Equations
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The Attempt at a Solution
I have the solution but I do not understand it.
"If (X^2, Y^2) would be distributed uniformly in {(x,y): 0 <= x <= 1,
0 <= y <= x^2}, then in particular,
P(Y^2 > (X^2)^2) = 0"
This makes sense, I doubt I'd try proving the new r.v wasn't distributed uniformly in the new interval in this way, but OK.
Continuing..
"...However: P(Y^2 > (X^2)^2) >= P(X <= 0.1, Y <= -0.9) = 2*(0.1^2)/2 = 0.01"
How in heaven's name the second inequality was derived? I do not understand this and the choice of the numbers ...
Please help. :)