Chapter 7
The probability of an event occurring is 1 minus the probability that it doesn't occur P(A) = 1- P(A^c)
Complement rule
When the probability comes from the long-run relative frequency of the event's occurrence, it is an empirical probability.
Empirical probability
to find the probability of an event from a conditional distribution we write? and pronounce it?
P(B|A) and say "the probability of B given A"
Two events are _____ if the fact that one event occurs does not change the probability of the other. Event A and B are ______ when P(B|A) = P(B)
Independence
P(B|A) = P(A and B) / P(A) has to be greater than zero to work
conditional probability
For any two events, A and B, the probability of A or B is: P (A or B) = P(A) + P(B) - P(A and B) (Does not require disjoint events)
general addition rule
For any two events, A and B, the probability of A and B is: P(A and B) = P(A) X P(B|A)
general multiplication rule
The probability that two events both occur
joint probabilities
States that the long-run relative frequency of repeated, independent events settles down to the true relative frequency as the number of trails increases
law of large numbers
The probability of an event is is?
long-run relative frequency
In a joint probability table a marginal probability is the probability distribution of either variable separately, usually found in the rightmost column or bottom row of the table.
marginal probability
For two independent events A and B, the probability that both A and B occur is the product of the probabilities of the two events. P(A and B) = P(A) x P(B), provided that A and B are independent.
multiplication rule
when the probability is subjective and represents your personal degree of belief
personal probability
The probability of the entire sample space must be 1: P(S) = 1
probability assignment rule
The collection of all possible outcome values. The sample space has a probability of 1
sample space
When the probability comes from a mathematical model
theoretical probability
A probability is a number between 0 and 1. For any event A, ?
0 less than or equal to P(A) less than or equal to 1
If A and B are disjoint events, then the probability of A or B is P(A or B) = P(A) + P(B)
addition rule
A phenomenon consists of trials. Each trial has an outcome. Outcomes combine to make events.
:D
Two events are disjoint if they share no outcomes in common. If A and B are disjoint, then knowing that A occurs tells us that B cannot occur. Also called mutually exclusive
disjoint events