Ch. 6: Discrete Random Variables

Question 1

a variable whose value is a numerical value that is determined by the outcome of an experiment

Answer 1

random variable

Question 2

What are the 2 types of random variables?

Answer 2

1. Discrete
2. Continuous

Question 3

What type of random variable is this?
Possible values can be counted or listed (basically, this is finite); a random variable that assumes countable values

Answer 3

Discrete random variable
(something we can count)

Question 4

What type of random variable is this?
May assume any numerical value in one or more intervals; something we can measure

Answer 4

Continuous random variable

Question 5

For the following examples, is it discrete random variable or continuous random variable?
1. The waiting time for a credit card authorization.
2. The number of defective units in a batch of 20.
3. A listener rating (on a scale of 1 to 5) in an AccuRating music survey.
4. The interest rate charged on a business loan.

Answer 5

1. Continuous random variable
2. Discrete random variable
3. Discrete random variable
4. Continuous random variable

Question 6

What are the 2 types of visualizations we can make for probability distribution of a DISCRETE random variable?

Answer 6

1. Bar graph
2. Pie chart

Question 7

What are the 4 diagrams we can make for probability distribution of a CONTINUOUS random variable?

Answer 7

1. Histogram
2. Line graph
3. Stem and leaf
4. Scatter plot
   (etc.)

Question 8

What are the 3 discrete probability distributions?

Answer 8

1. Binomial
2. Poisson
3. Hyper geometric

Question 9

What are the 3 continuous probability distributions?

Answer 9

1. Normal
2. Uniform
3. Exponential

Question 10

Temperature, height, interest rates, and weight are examples of (discrete/continuous) random variables.

Answer 10

continuous

Question 11

T or F: Bars joined together on a graph is to tell it’s continuous.

Answer 11

True

Question 12

• A continuous random variable is one which takes a(n) (finite/infinite) number of possible values.
• Continuous random variables are usually __________.

Answer 12

• infinite
• measurements

Question 13

Look in camera roll at 6.3 picture for more examples of discrete and continuous random variables.

Answer 13

Ok

Question 14

The _________ ________ of a discrete random variable is a table, graph or formula that gives the probability associated with each possible value that the variable can assume.

Answer 14

probability distribution (called a discrete probability distribution)

(KNOW THIS DEFINITION; write down on cheat sheet)

Question 15

What are the 2 Discrete Probability Distribution Properties?

Answer 15

1. For any value x of the random variable, p(x) ≥ 0
2. The probabilities of all the events in the sample space must sum to 1, that is… the sum of all the probabilities must = to 1.

(look at camera roll for these properties and write on cheat sheet; need to know these)

Question 16

Shoe size is an example of (discrete/continuous) random variable.

Answer 16

discrete

(can COUNT how many people have number of shoe size)

Question 17

Look at example 6.2 in camera roll for discrete random probability practice.

Answer 17

Ok
(good example to look over; 3 pics total)

Question 18

The mean/expected value/average value (all mean the same thing) of a discrete random variable x is:

Answer 18

Mean = (sum of all x) x (p(x))

(Sum of all x times p(x))
(look in camera roll for this formula and write on cheat sheet)

Question 19

______ is the value expected to occur in the long run and on average.

Answer 19

Mean (μ)

Question 20

Look at example 6.3 in camera roll for how to calculate mean for discrete random variables.

Answer 20

ok
(need to look at and maybe write on cheat sheet)

Question 21

The _______ is the average of the squared deviations of the different values of the random variable from the expected value.

Answer 21

variance

Question 22

What is the formula to find variance of a discrete random variable?

Answer 22

Look in camera roll for this formula and write on cheat sheet. Can’t type on here.

Question 23

What is the formula for calculating standard deviation for discrete random variables?

Answer 23

square root of variance

Question 24

The _________ and ______ ______ measure the spread of the values of the random variable from their expected value (or mean).

Answer 24

variance; standard deviation

(Ex: if the variance is 9, the value of standard deviation would be 3 bc you take the square root of 9 which = 3)

Question 25

Look at example 6.5 in camera roll for example of how to calculate variance for discrete random variables.

Answer 25

Ok (prob write on cheat sheet too)

Question 26

Look at page in camera roll titled "Plus or Minus Std. Dev. Example" to review how to calculate plus or minus 1,2,or 3 standard deviations, and then find the probability between these standard deviations.

Answer 26

Ok (write something about this on cheat sheet; 3 pages total)

Question 27

- A __________ _________ can be thought of as simply the probability of a SUCCESS or FAILURE outcome in an experiment or survey that is repeated multiple times. - The binomial is a type of distribution that has ______ possible outcomes.

Answer 27

- binomial distribution - two (ex: a coin toss has only two possible outcomes-- heads or tails and taking a test could have two possible outcomes-- pass or fail.)

Question 28

T or F: With binomial distribution, we will only have 2 outputs.

Answer 28

True (either success or fail)

Question 29

What are the 4 properties of binomial distribution (aka the four characteristics of a binomial experiment)?

Answer 29

1.) Experiment consists of n identical trials. 2.) Each trial results in either "success" or "failure" (2 outputs). 3.) Probability of success, p, is constant from trial to trial. - The probability of failure, q, is 1-p 4.) Trials are independent (important) (KNOW ALL THESE!!)

Question 30

The Binomial Distribution: If x is the total number of successes in n trials of a binomial experiment, then x is a __________ _________ variable.

Answer 30

binomial random

Question 31

T or F: An example of binomial distribution is customers apply for credit card. There is only two options, which is approved (success) or disapproved (fail).

Answer 31

True

Question 32

Look in camera roll for formula for binomial distribution.

Answer 32

Ok (if needing to understand better, look at examples 6.6 and 6.7 on ipad)

Question 33

How do you calculate mean for a binomial random variable?

Answer 33

Mean = n x p (n = number of trials) (p = success)

Question 34

How do you calculate variance for a binomial random variable?

Answer 34

Variance = n x p x q (n = number of trials) (p = success) (q = failure, or 1-p)

Question 35

How do you calculate standard deviation for a binomial random variable?

Answer 35

Take the square root of the variance formula for binomial random variables (square root of n x p x q)

Question 36

Poisson distributions are used by businessmen to make ________ about the number of customers or sales on certain days or seasons of the year. With the Poisson distribution, companies can adjust _______ to demand in order to keep their business earning good profit. In addition, waste of ________ is prevented.

Answer 36

forecasts; supply; resources

Question 37

When do we use Poisson Distribution?

Answer 37

When we are considering the number of times an event occurs OVER AN INTERVAL OF TIME OR SPACE (ex: the number of customers who arrive at the checkout counters of a grocery store in one hour, the number of major fires in a city during the next two months, the number of dirt specks found in one square yard of plastic wrap, etc.)

Question 38

The Poisson Distribution: Consider the number of times an event occurs over an interval of time or space, and assume that: 1. ? 2. ?

Answer 38

1. The probability of occurrence is the same for any intervals of equal length. 2. The occurrence in any interval is independent of an occurrence in any non-overlapping interval.

Question 39

If x= the number of occurrences in a specified interval, then x is a ______ _______ ________.

Answer 39

poisson random variable

Question 40

For Poisson Distribution, ______ is the expected number of occurrences during a specified interval.

Answer 40

mean

Question 41

What is the formula Poisson Distribution?

Answer 41

In camera roll (2 pics, one with formula and one with example table)... write formula on cheat sheet. (On exam, will be given a table, and we can find the probabilities since some calculators may not be able to do this formula.)

Question 42

If x is a Poisson random variable with parameter m, then: 1. Mean = 2. Variance = 3. Standard Deviation =

Answer 42

1. μ 2. μ (variance is same as mean) 3. square root of variance (AKA square root of mean) (look at camera roll for these formulas and write on cheat sheet)