Chapter 4 Statistic

Combinations rule

A combination is a selection of all or part of a set of objects, without regard to the order in which they were selected. This means that XYZ is considered the same combination as ZYX. The number of combinations of n objects taken r at a time is denoted by nCr.

More than two mutually exclusive events

Can be extended to apply to the situation in which we have more than two events, all which are mutually exclusive to all the other events.

Statistical experiment

Can be thought of as any random activity that result in a definite outcome.

P (A | B)

P(A, gives B) as "probability of A gives B," If A and B are dependent events, then P(A)Not equal P(A, gives B) because the occurrence of event B has changed the probability that event A will occur. A standard notation for P(A, gives B) is P(A | B).

Probability of A or B

Probability of A or B (1 of 3) If events A and B are mutually exclusive, then the probability of A or B is simply: p(A or B) = p(A) + p(B).

Equally likely outcomes

Probability of event= Number of outcomes favorable to event/ Total number of outcomes

Relative frequency

Probability of event= relative frequency f/n, where f is the frequency of the event occurrence in a sample of n observations.

More than two independent events

The multiplication rule for independent events extends to more than two independent event.

Conditional probability

The probability of an event ( A ), given that another ( B ) has already occurred.

Dependents event

Two events are dependent if the outcome or occurrence of the first affects the outcome or occurrence of the second so that the probability is changed.

Independent events

Two events are independent if the occurrence or nonoccurrence of one event does not change the probability that the other event will occur.

Probability of A and B

Two events are mutually exclusive or disjoint if they cannot occur at the same time. The probability that Event A occurs, given that Event B has occurred, is called a conditional probability. The conditional probability of Event A, given Event B, is denoted by the symbol P(A.

Event A and B

Two events are mutually exclusive or disjoint if they cannot occur at the same time. The probability that Event A occurs, given that Event B has occurred, is called a conditional probability. The conditional probability of Event A, given Event B, is denoted by the symbol P(A. B).

Event A or B

Two events are mutually exclusive or disjoint if they cannot occur at the same time. The probability that Event A occurs, given that Event B has occurred, is called a conditional probability. The conditional probability of Event A, given Event B, is denoted by the symbol P(A. B).

Mutually exclusive events

Two events are mutually exclusive or disjoint if they cannot occur together. In particular, events A and B are mutually exclusive if P(A and B)=0

Intuition

Incorporates past experience, judgment, or opinion to estimate the likelihood of an event.

Event

Is a collection of one or more outcomes of a statistical experiment or observation.

Simple event

Is one particular outcome of a statistical experiment.

Complement of event A'

Is the event that A doe snot occur. A' designates the complement of event A. 1. P(A)+P(A')=1 2.P(event A does not occur)= P(A')=1-P(A)

Probability of event A, P(A)

P(A) read "P and A," denotes the probability of event A If P(A)=1, event A is certain to occur If P(A)=0, event A is certain not to occur

Permutations rule

A permutation is an arrangement of all or part of a set of objects, with regard to the order of the arrangement. This means that XYZ is considered a different permutation than ZYX. The number of permutations of n objects taken r at a time is denoted by nPr.

Multiplication rule of counting

In combinatorics, the rule of product or multiplication principle is a basic counting principle (a.k.a. the fundamental principle of counting). Stated simply, it is the idea that if there are a ways of doing something and b ways of doing another thing, then there are a. b ways of performing both actions.

Law of large numbers

In the long run, as the sample size increases and increases, the relative frequencies of outcomes get closer and closer to the theoretical (or actual) probability value.

Multiplication rules of probability ( for independent and dependent)

P(A and B) =P(A)P(B) P(A and B)= P(A)P(B | A) P(A and B)= P(B)P(A | B)

Addition rules (for mutually exclusive and general events)

P(A and B)= P(A)+P(B)

Event A | B

P(A and B)= P(A)P(B)

Factorial notation

The factorial of a natural number n is the product of the positive integers less than or equal to n. The factorial of a non-negative integer n, denoted by n! and pronounced 'n factorial'.

Sample space

The set of all simple event constitutes the sample space of an experiment.

Basic probability rules

There are three basic rules associated with probability: the addition, multiplication, and complement rules. The addition rule is used to calculate the probability of event A or event B happening; we express it as: P(A or B) = P(A) + P(B) - P(A and B)

Tree diagram

There are two "branches" (Heads and Tails) The probability of each branch is written on the branch. The outcome is written at the end of the branch.