Quiz #2

1. Quiz #2 • Grades: • Total: 45 • Avg: 31 • Median: 29

2. 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.

3. 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)

4. 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

5. 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?

6. Q4: write an FSA for Regex Regex is (a|b)+ c* d? b+ Regex is (a|b)+ (c|d)* e? f+

7. Q5: draw an FST { (a2n c*, bn) | n>=0 }  {(an, d* b2n+1) | n>= 0}