This preview shows page 1. Sign up to view the full content.
Unformatted text preview: is just a single
equation that can be true even if A and B are not physically independent.
Example 2.4.2 Consider a probability experiment related to the experiment discussed in Section
1.3, in which a fair coin is ﬂipped and a die is rolled, with N denoting the side showing on the
coin and X denoting the number showing on the die. We should expect the event {N = H }
to be independent of the event {X = 6}, because they are physically independent events. This
independence holds, assuming all twelve outcomes in Ω are equally likely, because then P {N =
H } = 6/12, P {X = 6} = 2/12, and P {N = H, X = 6} = 1/12, so P {N = H, X = 6} = P {N =
H }P {X = 6}. More generally, any event involving only X is independent of any event involving
only N. Example 2.4.3 Suppose the probability experiment is to roll a single die. Let A be the event
that the outcome is even, and let B be the event that the outcome is a multiple of three. Since
these events both involve the outcome of a single role of a die, we...
View
Full
Document
 Spring '08
 Zahrn
 The Land

Click to edit the document details