Quiz

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(AB,C) P(AC)
• P(BA,C) P(BC)
• P(A,BC) P(BC) P(AC)
• 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 ngt0
• S ? a S b ²
• L2 a2n bn ngt 0
• S ? a a S b ²
• L3 a2n1 c bn ngt 0
• S1 ? a a S1 b S2
• S2 ? c S2 ²
• S ? a S1

5
Q3 (cont)

• L3 a2n1 c bn ngt 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 (ab) c d? b
• Regex is (ab) (cd) e? f

7
Q5 draw an FST

• (a2n c, bn) ngt0 ? (an, d b2n1) ngt
  0