Suppose Xi for i = 1, 2, 3 are independent and identically distributed random variables whose probability mass functions are Pr[Xi = 0] = Pr[Xi = 1] = 1/2 for i = 1, 2, 3. Define another random variable Y = X1 X2 ⊕ X3, where ⊕ denotes XOR. Then Pr[Y = 0 ⎪ X3 = 0] = ____________.

Suppose Xi for i = 1, 2, 3 are independent and identically distributed

1.	Suppose Xi for i = 1, 2, 3 are independent and identically distributed random variables whose probability mass functions are Pr[Xi = 0] = Pr[Xi = 1] = 1/2 for i = 1, 2, 3. Define another random variable Y = X1 X2 ⊕ X3, where ⊕ denotes XOR. Then Pr[Y = 0 ⎪ X3 = 0] = ____________.
A.	0.75
B.	0.50
C.	0.85
D.	0.25
Answer» B. 0.50

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