Artificial Intelligence: A Modern Approach
3rd Edition
ISBN: 9780136042594
Author: Stuart Russell, Peter Norvig
Publisher: Prentice Hall
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Expert Solution & Answer
Chapter 3, Problem 4E
Explanation of Solution
Formulation for a planar map:
- The goal state has the numbers in a certain order, which is measured as starting at the upper left corner, then proceeding left to right, and when we reach the end of a row, going down to the leftmost square in the row below.
- For any other configuration besides the goal, whenever a tile with a greater number on it precedes a tile with smaller number, the two tiles are said to be inverted.
Proposition:
- For a given puzzle configuration, let “N” denote the sum of the total number of inversions and the row number of the empty square.
- “Nmod2” is invariant under any legal move.
- After a legal move an odd “N” remains odd whereas an even “N” remains even.
- The goal state with no inversions and empty square in the first row, has “N=1”, and can only be reached from starting states with even “N”...
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Students have asked these similar questions
CT ser.
Pick one million sets of 12 uniform random numbers between 0 and 1. Sum up the
12 numbers in each set. Make a histogram with these one million sums, picking some
reasonable binning.
You will find that the mean is (obviously?) 12 times 0.5 = 6. Perhaps more surprising,
you will find that the distribution of these sums looks very much Gaussian (a "Bell
Curve"). This is an example of the "Central Limit Theorem", which says that the
distribution of the sum of many random variables approaches the Gaussian distribution
even when the individual variables are not gaussianly distributed.
mean
Superimpose on the histogram an appropriately normalized Gaussian distribution of
6 and standard deviation o = 1. (Look at the solutions from the week 5
discussion session for some help, if you need it). You will find that this Gaussian works
pretty well.
Not for credit but for thinking: why o = 1 in this case? (An explanation will come
once the solutions are posted).
Given a deck of 52 playing cards, we place all cards in random order face up next to each other.
Then we put a chip on each card that has at least one neighbour with the same face value (e.g., on
that has another queen next to it), we put a chip. Finally, we collect all chips that were
each
queen
placed on the cards.
For example, for the sequence of cards
A♡, 54, A4, 10O, 10♡, 104, 94, 30, 3♡, Q4, 34
we receive 5 chips: One chip gets placed on each of the cards 100, 10♡, 104, 30, 3♡.
(a) Let p5 be the probability that we receive a chip for the 5th card (i.e., the face value of the 5th
card matches the face value of one of its two neighbours). Determine p5 (rounded to 2 decimal
places).
(b) Determine the expected number of chips we receive in total (rounded to 2 decimal places).
(c) For the purpose of this question, you can assume that the expectation of part (b) is 6 or smaller.
Assume that each chip is worth v dollars. Further, assume that as a result of this game we receive
at least…
Chapter 3 Solutions
Artificial Intelligence: A Modern Approach
Ch. 3 - Explain why problem formulation must follow goal...Ch. 3 - Prob. 2ECh. 3 - Prob. 3ECh. 3 - Prob. 4ECh. 3 - Prob. 5ECh. 3 - Prob. 6ECh. 3 - Prob. 8ECh. 3 - Prob. 9ECh. 3 - Prob. 10ECh. 3 - Prob. 11E
Ch. 3 - Prob. 12ECh. 3 - Prob. 13ECh. 3 - Prob. 14ECh. 3 - Prob. 15ECh. 3 - Prob. 16ECh. 3 - Prob. 17ECh. 3 - Prob. 18ECh. 3 - Prob. 20ECh. 3 - Prob. 21ECh. 3 - Prob. 22ECh. 3 - Trace the operation of A search applied to the...Ch. 3 - Prob. 24ECh. 3 - Prob. 25ECh. 3 - Prob. 26ECh. 3 - Prob. 27ECh. 3 - Prob. 28ECh. 3 - Prob. 29ECh. 3 - Prob. 31ECh. 3 - Prob. 32E
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