Quiz 2
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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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Quiz #2

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Quiz 2

Quiz #2

  • Grades:

    • Total: 45

    • Avg: 31

    • Median: 29


Q1 conditional independence

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

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

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

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

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

Q5: draw an FST

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


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