Reading:

• R&N: 1.1,3-4; 26.1-2; Turing's "Computing Machinery and Intelligence" (link on course webpage)

FORMAT (applicable for all 391 assignments):

• Use standard sheets of paper (8.5 by 11 inches)
• Use a corner STAPLE to attach multiple sheets. Please, no paper clips, tape, or folding over.
• Perform all work neatly. When asked to write a paragraph (as in 1.1-5, G1.1 below), they should be typed (e.g., using a computer).
• 491 Students: Complete 491 portions on separate, stapled sheets. Don't forget your name.

The next five problems are taken from R&N: pages 30-31. Write a paragraph for each of them (10 points each).
Answers for 1.1-5 must be typed.

Problem 1.1 [10 points]

Problem 1.2 [10 points]

Problem 1.3 [10 points]

Problem 1.4 [10 points]

Problem 1.5 [10 points]

Problem 1.6 [20 points]

Formulate a simple cognitive model for addition of pairs of integers. Test it on a few examples. Implement it using a programming language of your choice. Turn in your code and some example input/output pairs.

How might you modify or use your model as part of a cognitive model of multiplication?

Problem 1.7 [30 points]

1. Toss a coin 31 times and record the outcome (as a string of H and T);
2. Compute the experimentally observed probability of heads over tosses 1 through 20;
3. Compute the Markov chain transition probabilities over the first 21 tosses (viz., the first 20 transitions).
4. Repeat (a)-(c) above with a sequence verbally derived from a friend not in the class who does not know the underlying model you are trying to construct.
5. Using any language you wish, implement a computer program to simulate a run of 10 tosses of the Markov chain starting at an arbitrary initial state: H or T.
6. Test your progam on its ability to predict the ten tosses (nos. 22 to 31) of both your coin and your friend.
7. Comment on your results.

Problem G1.1 [20 points]

Problem 1.7 of R&N. This answer must be typed and on a separarate sheet from the above.