Ch 5 Flashcards
(19 cards)
What is a random process?
Generates outcomes that are determined purely by chance.
What is probability?
The probability of any outcome of a random process is a number between 0 and 1 that describes the proportion of times the outcome would occur in a very long series of trials.
What is the law of large numbers?
Says that if we observe more and more trials of any random process, the proportion of times that a specific outcome occurs approaches its probability.
What is a simulation?
Imitates a random process in such a way that simulated outcomes are consistent with real-world outcomes.
What is a probability model?
A description of some random process that consists of two parts: a list of all possible outcomes and the probability for each outcome.
What is sample space?
The list of all possible outcomes.
What is an event?
Any collection of outcomes from some random process.
What does the complement rule state?
The complement rule says that P(A’) = 1 - P(A), where A’ is the complement of event A; that is, the event that A does not occur.
What are mutually exclusive (disjoint) events?
Two events A and B are mutually exclusive if they have no outcomes in common and so can never occur together—that is, if P(A and B) = 0.
What is the addition rule for mutually exclusive events?
For A and B, P(A or B) = P(A) + P(B).
What is the general addition rule?
If A and B are any two events resulting from some random process, the general addition rule says that P(A or B) = P(A) + P(B) - P(A and B).
What is a Venn diagram?
Consists of one or more circles surrounded by a rectangle. Each circle represents an event. The region inside the rectangle represents the sample space of the random process.
What is the intersection of events A and B?
The event ‘A and B’ is called the intersection of events A and B. It consists of all outcomes that are common to both events, and is denoted A ∩ B.
What is the union of events A and B?
The event ‘A or B’ is called the union of events A and B. It consists of all outcomes that are in event A or event B, or both, and is denoted A ∪ B.
What is conditional probability?
The probability that one event happens given that another event is known to have happened. The conditional probability that event A happens given that event B has happened is denoted by P(A|B).
What are independent events?
A and B are independent events if knowing whether or not one event has occurred does not change the probability that the other event will happen.
What is the general multiplication rule?
For any random process, the probability that events A and B both occur can be found using the general multiplication rule: P(A and B) = P(A) * P(B|A).
What is a tree diagram?
Shows the sample space of a random process involving multiple stages. The probability of each outcome is shown on the corresponding branch of the tree.
What is the multiplication rule for independent events?
If A and B are independent events, the probability that A and B both occur is P(A and B) = P(A) * P(B).
