- #1
CantorSet
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Suppose X and Y are continuous random variables with the joint pdf [tex]f_{xy}(x,y)[/tex] on the [tex][0,1] \times [0,1][/tex] square.
Is the probability [tex]P(X = Y)[/tex] then equal to zero since probability here is a volume, and the set that satisfies [tex]P(X = Y)[/tex] is a plane?
Supposing it's not zero, when I tried to evaluate it with the integral
[tex] \int_{0}^{1} f_{xy}(t,t)\sqrt2dt[/tex]
(basically, just a line integral) the answer seems way too big.
Any thoughts from the folks out there?
Is the probability [tex]P(X = Y)[/tex] then equal to zero since probability here is a volume, and the set that satisfies [tex]P(X = Y)[/tex] is a plane?
Supposing it's not zero, when I tried to evaluate it with the integral
[tex] \int_{0}^{1} f_{xy}(t,t)\sqrt2dt[/tex]
(basically, just a line integral) the answer seems way too big.
Any thoughts from the folks out there?