A. Questions for Submission
1.1 What kind of thing is a probability?
How would you explain what a "probability" is to a friend who had never heard of the concept? As an example, discuss what it might mean to say, "The probability of a drunkard walking left or right is 1/2." Is it a statement about your degree of belief? Or a propensity? Or a relative frequency? Explain your thinking.
1.2 Properties of Random Walks
- Can we make accurate predictions about a single drunkard that leaves the pub and follows a random walk for 20 steps before collapsing? How does this change if a group of 100 drunkards do this?
- Suppose the 100 drunkards each walk 40 steps instead of 20 before collapsing. How does their distribution change? Explain.
B. For Further Thought (Optional)
- What meanings (there may be more than one) does the word 'random' have in common English? Compare this to our use of the word 'random' in the definition of a random walk: to what extent are they the same? To what extent are they different?
- The chart below shows how the sum total price of all the stocks listed in the New York Stock Exchange changed during the first day of this course. What would have to be true for this price to be describable in terms of a random walk? Is this plausible? Discuss.
