Joint PDF of Random Variables X & Y -1 to 1

AI Thread Summary
The discussion focuses on the joint probability density function (PDF) of random variables X and Y defined as fx,y(x, y) = 1/2 for the range -1 ≤ x ≤ y ≤ 1, and 0 otherwise. Participants seek assistance in deriving the marginal PDF fy(y), the conditional PDF fx|y(x|y), and the expected value E[X|Y = y]. There is a specific inquiry about the limits for integration needed to calculate fy(y). The conversation emphasizes the need for clarity in the integration process to solve the problems effectively.
vptran84
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Hi, I really need help with joint PDF, if anyone can help, that would be super! :smile:

Random Variables X and Y have joint PDF
fx,y (x, y) = 1/2 if -1 <= x <=y <= 1, and it is 0 otherwise

a) what is fy (y)?

b) what is fx|y (x|y)?

c) what is E[X|Y = y]?
 
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Please show some work, first.
 
for part A) i know ur suppose to take the integral with respect to dx, but I'm not sure what the limits are.
 

Thread 'Formal derivation of statement from Peano Arithmetic system'

I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...
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