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Quiz #2

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- Grades:
- Total: 45
- Avg: 31
- Median: 29

- The definition of A and B are conditionally independent given C
- P(A|B,C) = P(A|C)
- P(B|A,C) = P(B|C)
- P(A,B|C) = P(B|C) P(A|C)
- Once we know C, knowing B does not help us to predict the value of A; that is, C provides all the information that B could provide about A.
- P(xn | x1, …, xn-1) = P(xn | xn-1); that is, xn is conditionally independent from x1, …, xn-2, given xn-1.

P(X1, …, Xn)

= P(X1) P(X2) … P(Xn) (?)

= P(X1) P(X2 | X1) … P(Xn | Xn-1) (?)

= P(X1) P(X2 | X1) … P(Xn | X1, …, Xn-1)

- L1 = {an bn | n>=0}
S a S b | ²

- L2 = {a2n bn | n>= 0}
S a a S b | ²

- L3 = {a2n+1 c* bn | n>= 0}
S1 a a S1 b | S2

S2 c S2 | ²

S a S1

- L3 = {a2n+1 c* bn | n>= 0}
S S1 S2 S3

S1 a S1 | ²

S2 c S2 | ²

S3 b S3 | ²

Is it correct?

Regex is (a|b)+ c* d? b+

Regex is (a|b)+ (c|d)* e? f+

{ (a2n c*, bn) | n>=0 } {(an, d* b2n+1) | n>= 0}