Artificial Intelligence: A Modern Approach
Artificial Intelligence: A Modern Approach
3rd Edition
ISBN: 9780136042594
Author: Stuart Russell, Peter Norvig
Publisher: Prentice Hall
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Chapter 7, Problem 3E

a.

Explanation of Solution

Recursive algorithm

  • The language has built-in Boolean operators not,and,or and if.
  • The algorithm is

  function PL-TRUE?(s,m) returns true or false

if s = True then return true

  else if s = False then return false

  else if SYMBOL?(s) then return LOOKUP(s,m)

  else...

b.

Explanation of Solution

Sentences

  • All the sentences can be determined to be true or false...

c.

Explanation of Solution

Truth value

  • A general algorithm for partial models must handle the empty partial model, with no

  assignments...

d.

Explanation of Solution

Modification of algorithm

  • It helps if and and or evaluate their arguments in sequence, terminating on false or true arguments, respectively.
  • In that case, the algorithm already has the desired propertie...

e.

Explanation of Solution

Modified algorithm makes TT-Entails or not

  • Early termination in Boolean operators will provide a very substantial speedup...

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using r language for integration theta = integral 0 to infinity (x^4)*e^(-x^2)/2 dx (1) use the density function of standard normal distribution N(0,1) f(x) = 1/sqrt(2pi) * e^(-x^2)/2 -infinity <x<infinity as importance function and obtain an estimate theta 1 for theta set m=100 for the estimate whatt is the estimate theta 1? (2)use the density function of gamma (r=5 λ=1/2)distribution f(x)=λ^r/Γ(r) x^(r-1)e^(-λx) x>=0 as importance function and obtain an estimate theta 2 for theta set m=1000 fir the estimate what is the estimate theta2? (3) use simulation (repeat 1000 times) to estimate the variance of the estimates theta1 and theta 2 which one has smaller variance?
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