Quiz #2

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# Quiz #2 - PowerPoint PPT Presentation

Quiz #2. Grades: Total: 45 Avg: 31 Median: 29. Q1: conditional independence. 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)

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Presentation Transcript
Quiz #2
• Total: 45
• Avg: 31
• Median: 29
Q1: conditional independence
• 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.
Q2: chain rule

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)

Q3: write a CFG
• 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

Q3 (cont)
• 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?

Q4: write an FSA for Regex

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

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

Q5: draw an FST

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