[M2] Midterm (Identification) Flashcards
Is any activity or situation in which there is uncertainty about which of two or more possible outcomes will result.
chance experiment
The collection of all possible outcomes of a chance experiment is the ________ for the experiment.
sample space
It is a subset of a sample space.
event
Each outcome in a sample space is called an _________ or a _______ of the sample space, or simply a ______________.
element, member, sample point
In some experiments, it is helpful to list the elements of the sample space systematically
tree diagram
Sample spaces with a large or infinite number of sample points are best described by _______.
statement or rule method
The __________ of an event A with respect to S is the subset of all elements of S
that are not in A. We denote the complement of A by the symbol A.
complement
The _______ of two events A and B, denoted by the symbol A ∩ B, is the
event containing all elements that are common to A and B.
intersection
The ____ of the two events A and B, denoted by the symbol A ∪ B, is the event containing all the elements that belong to A or B or both.
union
Two events A and B are _______, if A ∩ B = φ, that is, if A and B have no elements in common.
mutually exclusive or disjoint
The relationship between events and the corresponding sample space can be
illustrated graphically
venn diagram
It is an arrangement of all or part of a set of objects.
permutation
Events that by definition cannot happen together.
Mutually exclusive events
If the occurrence of one event A does not affect, nor is affected by, the occurrence of another event B then we say that A and B are _______ events.
independent
The probability that event B will occur given that event A has already occurred
Conditional Probability: Dependent Events
If A and B are independent events then P(A ∩ B) = P(A) × P(B)
The probability of independent events A and B occurring is the product of the probabilities of the events occurring separately.
Multiplication Rule
A distribution showing the different values of a random variable with their corresponding probabilities.
probability distribution
The simplest of all discrete probability distributions. It is one where the random variable assumes each of its values with an equal probability.
Uniform Distribution
Most often an experiment consists of repeated trials, each with two possible outcomes that may be defined as a success or a failure. This referred to as the Bernoulli process and each trial is called a Bernoulli trial.
The Binomial Probability Distribution
If we let each trial to have more than 2 possible outcomes
multinomial distribution
It represents the number of trials needed
to obtain exactly k successes.; here, the number of successes is fixed, and the number of trials will vary from experiment to experiment.
Negative Binomial Distribution
a) The experiment consists of a series of n Bernoulli trials. The outcome of each trial can be identified as being either a “success” or a “failure”;
b) The trials are identified and independent so the probability of success, p, remains the same from trial to trial;
c) The number of trials needed to obtain the first success is denoted by
the random variable x.
Geometric Distribution
a) A random sample of size n is drawn without replacement and
without regard to order from a collection of N objects; and
b) Of the N objects, k may be classified as successes and the other N –
k as failures.
Hypergeometric Probability Distribution
Its probability distribution provides a good model for data that represents the number of occurrences of a specified event in a given unit of time or space.
Poisson Distribution
