Homework 8: Discrete Random Variables

1. Section 3.1, #2, 3.
2. An urn contains seven balls numbered 1 to 7. Two balls are drawn simultaneously. Let \(X\) be the larger of the two numbers drawn. Find \(f_X(x)\).
3. A fair die is tossed three times. Let \(X\) be the number of different faces that appear. Find \(f_X(x)\).
4. Five men and five women are ranked according to their scores on an examination. Assume that no two scores are alike and all \(10!\) possible rankings are equally likely. Let \(X\) denote the highest ranking achieved by a woman. (For instance, \(X=1\) if the top-ranked person is a woman.) Find \(f_X(x)\).
5. Let \(X\) be the difference between the number of heads and the number of tails when a coin is tossed \(n\) times. What are the possible values of \(X\)?
6. An elementary school has 3 sixth-grade classes, each consisting of 20 students. From these 60 sixth-grade students, a committee of 3 students is selected at random. Let the random variable \(X\) be the number of different classes the three committee members are from. (For example, \(X=3\) if the committee members are all from different classes.) What are the different values \(X\) can take? Find the probability function of \(X\).