Читать книгу Probability - Robert P. Dobrow - Страница 43

1 1.9 A sample space has four elements such that is twice as likely as , which is three times as likely as , which is four times as likely as . Find the probability function.

2 1.10 A sample space has four elements such that is ten times as likely as , which is four times as likely as . Finally, is as likely as and combined. Find the probability function.

3 1.11 A sample space has four elements. For the potential probability functions for the sample space below, state whether they are valid or not. Provide support for your response.....

4 1.12 A random experiment has three possible outcomes , , and , with1.13 What choice(s) of makes this a valid probability model?

5 1.13 Let and be two probability functions on . Define a new function such that Show that is a probability function.

6 1.14 Suppose are probability functions on Let be a sequence of numbers. Under what conditions on the 's willbe a probability function?

7 1.15 Let be a probability function on such that and for Let be a function on defined by For what value(s) of will be a valid probability function?