Stats Chapter 4 – Flashcards

Is the numerical measure of the likelihood that an event will occur. -A probability near zero indicates an event is unlikely to occur; a probability near 1 indicates an event is almost certain to occur. Figure 4.1 (pg.180)

Is a process that generates well-defined experimental outcomes. On any single repetition or trial, the outcome that occurs is determined completely by chance. As a result, the process of tossing a coin is considered a random experiment. (pg.180)

Is any process that generates well-defined outcomes.

The sample space for a random experiment is the set of all experimental outcomes. Ex. If we let S denote the sample space, we can use the following notation to describe the sample space. S= {Head, Tail} S= {1,2,3,4,5,6}

An experimental outcome. -An element of the sample space.

Is a graphical representation that helps in visualizing a multiple-step random experiment. Ex. Figure 4.2 & Figure 4.3

1.) The probability assigned to each experimental outcome must be between 0 and 1, inclusively. 2.) The sum of the probabilities for all the experimental outcomes must equal 1.0.

(gains of chance "gambling," equal probability) Assigning probabilities based on the assumption of *equally likely outcomes.* Ex. Rolling a Die (look @ notebook)

(Historical or Experimental Data) (based on data) Assigning probabilities based on *experimentation or historical data.* -Is appropriate when data are available to estimate the proportion of the time the experimental outcome will occur if the random experiment is repeated a large number of times.

(expert opinion, educated guess,not based on numbers/ not really any data) Assigning probabilities based on *judgement.* -Is most appropriate when one can not realistically assume that the experimental outcomes are equally likely and when little relevant data are available. ~We may use any information available, such as experience or intuition. After considering all available information, a probability value that expresses our "degree of belief" (on a scale from 0 to 1) that the experimental outcome will occur is specified. B/c subjective probability expresses a person's degree of belief, it is personal. Using the subjective method, different people can be expected to assign different probabilities to the same experimental outcome.

Is a collection of sample points. -The probability of any event is equal to the sum of the probabilities of the sample points in the event. -If we can identify all the sample points of an experiment and assign a probability to each, we can compute the probability of an event.

Is defined to b the event consisting of all sample points that are NOT in A. -The complement of A is denoted by A^c. Figure 4.4 (pg.195)

The UNION of A and B is the event containing ALL sample points belonging to A OR B OR BOTH. ~ The union is denoted by A U B (look @ notebook). Figure 4.5 (pg.196)

Given two events A and B, the INTERSECTION of A and B is the event containing the sample points to BOTH A AND B. ~ The intersection denoted by A n B (look @ notebook). Figure 4.6 (pg.196)

Provides a way to compute the probability of event A, or B, or both A & B occurring. P(A U B)= P(A)+P(B)- P(A n B) ^Intersection (look @ the notebook) -To understand the addition law intuitively, note that the first two terms in the addition law, P(A)+ P(B), account for all the sample points in A U B. However, because the sample points in the intersection A n Bare in both A and B, when we compute P(A)+ P(B), we are in effect counting each of the sample points in A n B twice. We correct for this over counting by subtracting P(A n B) (pg.197).

Two events are said to be mutually exclusive if the events have no sample points in common. -Two events are mutually exclusive if, when one event occurs, the other cannot occur. *Addition Law for MUTUALLY EXCLUSIVE EVENTS (pg.198)* Figure 4.7

The probability of an event given that another event has occurred. The conditional probability of A given B is denoted by P(A I B) (look @ the notebook) reads as "the probability of A given B." ~WE use the notation "I" to indicate that we are considering the probability of event A GIVEN the condition that event B has occurred. Formulas (pg.203) (look @ the notebook) Figure 4.8 (pg.203)

The probability of the intersection of two events. Table 4.5 (pg.202)

We note that the marginal probabilities are found by summing the joint probabilities in the corresponding row or column of the joint probability table. -The values in the margins of the joint probability table provide the probabilities of each event separately. Table 4.5 (pg.202)