Definitions (Weeks 6 & 7) Statistics

Combination

# of subsets of a given size r that differ from each other by at least 1 item. It disregards the order of the items in the subsets. The combinations of r items out of a set of n items is denoted as C^n/r = n! [r! (n-r)!]

Union

Disjunctive Probability may be thought of as union.

Permutation

Gives us the total # of orderings of a set or subset. If the set contains n items, the permutations of all n items is denoted as n! or n factorial. n! = (n-1) (n-2) (n-3)...(3)(2)(1.) Note that 0! = 1 P^n/n is the notation we use for permutations of n items taken n at a time. If only a subset of size r is ordered, the notation is P^n/r = n!/(n-r)!

Mutually Exclusive Events or Outcomes

If two events are mutually exclusive, their joint probability is zero because they cannot co-occur. For example, the probability of getting both a head and a tail on one flip of a coin is zero.

Simple Probability

It is used to indicate the likelihood of occurrence of an event. It can be calculated as relative, or percent frequency. P(A) = # A / Total

Intersection

Joint Probability may be thought of as intersection.

Joint Probability. What happens if two events are mutually exclusive? What happens if two events are joint?

Likelihood of co-occurrence of two or more events. It's denoted as: P(A and B). If two events are mutually exclusive, their joint probability is zero because they cannot co-occur. For example the probability of getting both a head and a tail on one flip of a coin is zero. P(AxB) = P(A) P(B|A) for joint events

Probability

The extent to which an event is likely to occur, measured by the ratio of the favourable cases to the whole number of cases possible.

Disjunctive Probability. What happens if A and B are mutually exclusive in P (A and B)?

The likelihood of either event A or event B or both occurring. P(A or B) = P(A) + P(B) - P (AxB) If P (A and B) are mutually exclusive, their joint probability is zero and the disjunctive probability simplifies to the sum of the individual probabilities: P (A or B) = P(A) + P (B)

Conditional Probability: What is it? What is it denoted as? What is the relationship between joint probability and conditional probability?

The likelihood of event B occurring given that event A has occurred. It is denoted as P(B|A). The relationship between joint probability and conditional probability is as follows: (P B|A) = P(AxB)/P(A)

Independent Events. If A and B are independent, what is P(A|B)? What is P(B|A)? What is the joint probability of independent events equal to?

Two events A and B are independent if the outcome of A does not influence the outcome of B and visa versa. P (A|B) = P (A) & P (B|A) = P (B) If A and B are independent. This means that the joint probability of independent events is equal to the product of their individual probabilities. P(AxB) = P(A) P(B) for independent events.

Binomial Distribution: What is it used to obtain? What does r take on? What 3 things are we assuming?

Used to obtain the likelihood of r "successes"/n trials. r takes on all values from 0 to n inclusive. We are assuming: 1. The trials are independent of each other 2. The probability of "success" on any given trial = p. 3. The probability of failure on any trial is q = 1-p