[M2] Midterm (Identification)

Question 1

Is any activity or situation in which there is uncertainty about which of two or more possible outcomes will result.

Answer 1

chance experiment

Question 2

The collection of all possible outcomes of a chance experiment is the ________ for the experiment.

Answer 2

sample space

Question 3

It is a subset of a sample space.

Answer 3

event

Question 4

Each outcome in a sample space is called an _________ or a _______ of the sample space, or simply a ______________.

Answer 4

element, member, sample point

Question 5

In some experiments, it is helpful to list the elements of the sample space systematically

Answer 5

tree diagram

Question 6

Sample spaces with a large or infinite number of sample points are best described by _______.

Answer 6

statement or rule method

Question 7

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.

Answer 7

complement

Question 8

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.

Answer 8

intersection

Question 9

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.

Answer 9

union

Question 10

Two events A and B are _______, if A ∩ B = φ, that is, if A and B have no elements in common.

Answer 10

mutually exclusive or disjoint

Question 11

The relationship between events and the corresponding sample space can be
illustrated graphically

Answer 11

venn diagram

Question 12

It is an arrangement of all or part of a set of objects.

Answer 12

permutation

Question 13

Events that by definition cannot happen together.

Answer 13

Mutually exclusive events

Question 14

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.

Answer 14

independent

Question 15

The probability that event B will occur given that event A has already occurred

Answer 15

Conditional Probability: Dependent Events

Question 16

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.

Answer 16

Multiplication Rule

Question 17

A distribution showing the different values of a random variable with their corresponding probabilities.

Answer 17

probability distribution

Question 18

The simplest of all discrete probability distributions. It is one where the random variable assumes each of its values with an equal probability.

Answer 18

Uniform Distribution

Question 19

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.

Answer 19

The Binomial Probability Distribution

Question 20

If we let each trial to have more than 2 possible outcomes

Answer 20

multinomial distribution

Question 21

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.

Answer 21

Negative Binomial Distribution

Question 22

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.

Answer 22

Geometric Distribution

Question 23

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.

Answer 23

Hypergeometric Probability Distribution

Question 24

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.

Answer 24

Poisson Distribution