Exam 2

Question 1

Properties of probabilities

Answer 1

1.) Each probability lies between 0 and 1
2.) Sum of all simple-event probabilities equal 1

Question 2

Conditional Probability

Answer 2

is the situation whereby probability of one event is influenced by that of another event

Question 3

P[A|B]

Answer 3

Probability of “event A given that B has occurred.”

Question 4

If the occurrence of an event B does not alter the occurrence of event A, then A and B are said to be ________

Answer 4

Independent
P[ A n B] = P[A] * P[B]

Question 5

A _______ is a picture of the possible outcomes of a procedure, shown as a line segments emanating from one starting point.

Answer 5

Tree Diagrams

Question 6

Union

Answer 6

A set that contains the elements in A, B or both

Question 7

Intersection

Answer 7

A set that contains only the elements that appear in both sets

Question 8

Complement

Answer 8

the opposite

Question 9

Mutually Exclusive ( or disjoint)

Answer 9

They have no elements in common

Question 10

Mutually Exhaustive

Answer 10

They contain all the elements of the universe

Question 11

What theorem describes the probability of an event, based on conditions that might be related to the event.

Answer 11

P(A|B) = P( A n B) / P(B)

Question 12

A permutation of a set of distinct objects is an ________

Answer 12

ordered arrangement of objects

Question 13

An ordered arrangement of r elements of a set is called an _______

Answer 13

r-permutation

Question 14

0! = ______

Answer 14

1

Question 15

How can the total probability of an event be obtained?

Answer 15

The total probability of an event can be obtained by summing the set of MUTUALLY EXCLUSIVE and EXHAISTIVE ways of the event occuring

Question 16

A _____ is an unordered sample (without replacement) from a given finite set

Answer 16

Combination

Question 17

An r-combination of elements of a set is an ____________ of r elements from a set

Answer 17

Unordered selection

Question 18

True or False:
A combination is a selection of k objects from a group of n object when order does matter

Answer 18

FALSE!!!

A combination is a selection of k objects from a group of n object when order DOES NOT matter

Question 19

A______________ is a variable that assumes numerical values associated with the random outcome of an experiment, where one (and only one) numerical values is assigned to each sample point.

Answer 19

Random Variable

Question 20

A_______is a probability value that has been revised by using additional information that is later obtained

Answer 20

posterior probability

Question 21

What does the PDF measure?

Answer 21

The PDF, fx(x), measures how likely a random variable is to lie at a particular value or how fast the CDF is increasing.

• represents the density of the probability at some point x

Question 22

The CDF, F(x), is defined as F(x) =

Answer 22

FX(x) = P[X less than or equal to x]

Question 23

True or False:
The derivative of the CDF is the PDF

Answer 23

TRUE

Question 24

CDF

Answer 24

is a probability and satisfies all the axioms and corollaries of probability

Question 25

mn rule (product rule)

Answer 25

For a sequence of two events in which the first event can occur m ways and the second event can occur n ways, the events together can occur a total of m n ways

Question 26

Discrete random variable

Answer 26

may assume a finite number of numerical values or an infinite sequence of values

Question 27

What are the three criteria to be considered a Bernoulli Distribution

Answer 27

1.) There must be only 2 possible outcomes 2.) Each outcome must have an invariant probability of occurring. i.e., the probability of success is usually denoted by p, and the probability of failure is denoted by q = 1 - p 3.) The outcome of each trial is completely independent of the outcome of any other trials.

Question 28

Binomial Distribution B(n,p)

Answer 28

Also has 2 outcomes- success or failure, True or False It is the probability of exactly k successes in n trials There must be k successes and (n-k) failures in the n trials, but the order in which the successes and failures occur is immaterial. Trials are independent

Question 29

Continuous Random Variable

Answer 29

Is a random variable that has an infinite number of possible values that is not countable

Question 30

Discrete probability distrubtion

Answer 30

provides the possible values of th RV and their corresponding probabilities. It is also called the probability mass function (PMF)

Question 31

PMF

Answer 31

the probability that the RV X is equal to x P[ X=x], is given a numerical value by the probability function

Question 32

Poisson Distribution

Answer 32

is the probability of exactly k successes in a "unit" or continuous time interval. It is used to determine the number of occurrences of an event in a certain time interval,e.g., rate of growth or decay

Question 33

Probability Density Function(PDF)

Answer 33

Measures how likely a random variable is to lie at a particular value or how fast the CDF increasing