18.44 Chapter Notes - Chapter 10: Mit Opencourseware
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18. 440 problem set 10: due may 9: from textbook chapter nine, problem/theoretical exercise 13: prove that if x can take on any of n possible values with respective probabilities p1, . , pn, then h(x) is maximized when pi = 1/n, i = 1, . , n. what is h(x) equal to in this case: problem/theoretical exercise 15: a coin having probability p = 2/3 of coming up heads is ipped 6 times. Compute the entropy of the outcome of this experiment. (an outcome is a full toss sequence, e. g. , {h, t, t, t, h, h}. : problem/theoretical exercise 17: show that, for any discrete random variable x and function f, H(f(x)) h(x): solve the following problems, suppose harriet has 15 dollars. Her plan is to make one dollar bets on fair coin tosses until her wealth reaches either 0 or 50, and then to go home. What is the probability that she will have.
