Sta2023 Test 2

For a discrete random variable x, the probability of any value of x will be between ________ and ________. The sum of the probabilities of all simple events in a probability distribution will always equal __________.

0 and 1, Sum= 1

The number of days it rains in a month in New York

Discrete

The number of persons allergic to penicillin

Discrete

Are the events "Has math anxiety" and "Person is female" independent or dependent? Detail the calculations you performed to determine this.

The events are dependent.

Describe the three conditions that must be satisfied to apply the Poisson probability distribution.

The following three conditions must be satisfied to apply the Poisson probability distribution. 1.x is a discrete random variable. 2.The occurrences are random. 3.The occurrences are independent.

Examples of discrete random variable

The number of days it rains in a month in NY The number of stocks a person owns The number of persons allergic to penicillin The number of horses owned by a farmer

Which of the following is an example of a discrete random variable?

The number of horses owned by a farmer

What name is given to a table that lists all of the values that a discrete random variable x can assume and their corresponding probabilities?

The probability distribution table.

Which of the following is not an example of a discrete random variable?

The time spent by a physician with a patient A) The number of days it rains in a month in New York B) The number of stocks a person owns C) The number of persons allergic to penicillin

Which of the following is not a condition of the binomial experiment?

There are only two trials

Which of the following is an example of a binomial experiment?

Tossing a coin 20 times and observing for a head or tail

For the probability distribution of a discrete random variable x, the sum of the probabilities of all values of x must be:

equal to 1

The mean of a discrete random variable is its:

expected value

Two independent events

have no effect on the occurrence of each other

Two equally likely events

have the same probability of occurrence

For the probability distribution of a discrete random variable, the probability of any single value of x is always

in the range 0 to 1

The probability of an event is always

in the range 0 to 1.0

A compound event includes

more than one outcome for an experiment

The parameters of the binomial probability distribution are

n and p

Give the 4 conditions necessary for a 'Binomial' Experiment:

n identical trials, 2 possible outcomes, trials are independent, values of p and q remain constant throughout experiment

Two independent events are

never mutually exclusive

The mean of a binomial distribution is equal to

np

The mean of a binomial distribution is equal to:

np

A random variable is a variable whose value is determined by the:

outcome of a random experiment

The binomial probability distribution is skewed to the left if

p >.5

The binomial probability distribution is symmetric if

p is equal to .50

The binomial probability distribution is symmetric if:

p is equal to 0.50

The binomial probability distribution is skewed to the right if

p<.5

The binomial probability distribution is symmetric if (a)p<.5

p=.5

The mean of a discrete random variable is the mean of its:

probability distribution

The standard deviation of a discrete random variable is the standard deviation of its:

probability distribution

The standard deviation of a binomial distribution is equal to

square root of npq

The standard deviation of a binomial distribution is equal to:

square root of npq

A continuous random variable is a random variable

that can assume any value in one or more intervals

A continuous random variable is a random variable:

that can assume any value in one or more intervals

A discrete random variable is a random variable

whose set of values is countable

A discrete random variable is a random variable:

whose set of values is countable

A random variable is a variable whose value is determined by the

Outcome of a random experiment

The counting method used when order matters

Permutation

The counting method used when order matters is called a ______________________. When order does not matter, we use ____________________

Permutation, Combinations

The mean of a discrete random variable is the mean of its

Probability distribution

The standard deviation of a discrete random variabel is the standard deviation of its

Probability distribution

Name and describe the three conceptual approaches to probability:

Relative frequency approach-experimental-based, p(x) = f/n (what you observe) Classical-theoretical, based on equally-likely outcomes (what you expect to happen) Subjective- probability based on one's opinions or previous experiences.

Examples of Binomial Experiment

Rolling a die 25 times and observing for an even or odd number Randomly selecting 50 items from a production line and observing if they are good or defective Rolling a die 20 times in observing for a number that is less than or equal to four or greater than four Tossing a coin 20 times and observing for a head or a tale

The set of all possible outcomes in an experiment is called the

Sample space

Which of the following is not a binomial experiment?

Selecting 50 adults and observing if they are in favor of an issue, against it, or have no opinion A) Rolling a die 25 times and observing for an even or odd number B) Randomly selecting 50 items from a production line and observing if they are good or defective C) Rolling a die 20 times and observing for a number that is less than or equal to 4 or greater than 4

The joint probability of two mutually exclusive events is always

0

For the probability distribution of a discrete random variable, the sum of the probabilities of all possible values of x is always

1.0

The sum of the probabilities of all final outcomes of an experiment is always

1.0

Briefly explain when a hypergeometric probability distribution is used.

A hypergeometric probability distribution is used to find probabilities for the number of successes in a fixed number of trials, when the trials are not independent (such as sampling without replacement from a finite population.)

Briefly explain the meaning of a random variable, a discrete random variable, and a continuous random variable. Give one example each of a discrete and a continuous random variable.

A variable whose value is determined by the outcome of a random experiment is called a random variable. A random variable that assumes countable values is called a discrete random variable. The number of cars owned by a randomly selected individual is an example of a discrete random variable. A random variable that can assume any value contained in one or more intervals is called a continuous random variable. An example of a continuous random variable is the amount of time taken by a randomly selected student to complete a statistics exam.

Which of the following pairs of events are mutually exclusive? A) Female and male B) Female and no C) Female and yes D) Male and no E) Male and yes F) No and yes

A) Female and male F) No and yes

The probability distribution table of a discrete random variable lists

All of the values that the random variable can assume and their corresponding probabilities

State the four conditions of a binomial experiment. Give one example of such an experiment.

An experiment that satisfies the following four conditions is called a binomial experiment. i.There are n identical trials. In other words, the given experiment is repeated n times, where n is a positive integer. ii.Each trial has two and only two outcomes. iii.The probability of p and q remain constant for each trial. iv.The trials are independent. In other words, the outcome of one trial does not affect the outcome of another trial. An example of a binomial experiment is flipping a coin many times and observing whether the outcome of each flip is a head or a tail.

Which of the following probability approaches can be applied only to experiments with equally likely outcomes?

Classical probability

The counting method when order does NOT matter

Combination

The height of a person

Continuous

The price of a house in Vero Beach

Continuous

The time spent by a physician with a patient

Continuous

Conditions of a binomial experiment

Each trial has two and only two outcomes p is the probability success, q is the probability failure and p+q=1 The trials are independent

The mean of a discrete random variable is its

Expected value

Describe 'independent' events

Independent events have no affect on each other. You must use the 'test for independence' to determine this if it is not given.

Describe 'mutually exclusive' events

Mutually Exclusive events cannot occur at the same time, they will contain no common elements or outcomes, and they are always dependent

The collection of all outcomes for an experiment is called

a sample space

A final outcome of an experiment is called

a simple event

The probability distribution table of a discrete random variable lists:

all of the values that the random variable can assume and their corresponding probabilities

For a discrete random variable X, the probability of any value of X is

always in the range of 0-1

For a discrete random variable x, the probability of any value of x is:

always in the range zero to 1

Two mutually exclusive events

cannot occur together