Let the joint pdf of random variables X and Y defined as: SA, 0< |æ|+ |y] < 1 |0, otherwise. fx,Y (r, y) = a) What is the value of A? b) What is the marginal pdf of X? c) Are X and Y independent? Prove this. d) Calculate the conditional density fr (y |æ). Prove that it is a valid pdf.

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Let the joint pdf of random variables X and Y defined as:
J 4, 0<|피 + \yl < 1
20,
fx,y (x, y) :
otherwise.
a) What is the value of A?
b) What is the marginal pdf of X?
c) Are X and Y independent? Prove this.
d) Calculate the conditional density fy (y |x). Prove that it is a valid pdf.
Transcribed Image Text:Let the joint pdf of random variables X and Y defined as: J 4, 0<|피 + \yl < 1 20, fx,y (x, y) : otherwise. a) What is the value of A? b) What is the marginal pdf of X? c) Are X and Y independent? Prove this. d) Calculate the conditional density fy (y |x). Prove that it is a valid pdf.
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