6.1 Discrete Random VariablesObjectives:By the end of this section, I will beable to…

1) Identify random variables.2) Explain what a discrete probability

distribution is and construct probability distribution tables and graphs.

3) Calculate the mean, variance, and standard deviation of a discrete random variable.

Making Decisions• We are constantly making

decisions. What should I wear today? What girl should I ask to the prom? Should I smoke that cigarette?

• One thing to do is to write out all the possible outcomes to a situation.

Random Variable

• A variable whose values are determined by chance.

• It must be RANDOM

TWO TYPES OF R.V.

• Continuous random variable• When the random variable can

take infinitely many values, usually an interval.

• Discrete random variable• When the random variable can be

counted or listed

Is it Discrete RV or Continuous RV?

1) Three cards are selected from a deck of cards. We want to know how many aces can be obtained.

2) Let x be the number of people who are going to attend Disney on Ice.

3) A nurse is taking your blood pressure. Let y be your systolic blood pressure.

Discrete RV

Discrete RV

Continuous RV

Probability Distribution• It is a table that shows the results of your

experiment• The SUM of the PROBABILITES must = 1

Random Variable, x p(x)0 0.121 0.282 0.043 0.234 0.33

0.12 + 0.28 + 0.04 + 0.23 + 0.33 = 1.00

Probability Distribution• How many siblings do you have?

Random Variable, x p(x)0123456

Probability Questions

• Answer the following using that chart:

1) p(x = 2)2) p(x > 2)3) p(x ≠ 4)4) p(x ≤ 3)5) p(not 1)

Mean, Variance, and Standard Deviation of a Probability Distribution

Mean, Variance, and Standard Deviation of a Probability Distribution

( )x x p x 2 ( )Variance x x p x

standard deviation = Variance

1) This is the only animal that can’t jump.

(Rhinoceros or an Elephant)

2) If Barbie were life-size she would be this

tall. (6’0 or 7’2)

3) It is the shortest complete sentence in the

English Language. (“No” or “Go”)

4) This part of your body never grows from

birth. (Eyes or Brain)

5) It is impossible to lead a cow upstairs or

downstairs?

6) Which do people fear more, death or spiders?

7) Women do this nearly twice as much as men,

shower or blink?

8) This animal is the slowest on Earth, tree sloth

or tortoise

1) This is the only animal that can’t jump.

(Elephant)

2) If Barbie were life-size she would be this

tall. (6’0)

3) It is the shortest complete sentence in the

English Language. (“Go”)

4) This part of your body never grows from

birth. (Eyes)

5) It is impossible to lead a cows

downstairs

6) Which do people fear more, spiders

7) Women do this nearly twice as much as

men, blink

8) This animal is the slowest on Earth, tree

sloth

• What was your score?

• Let’s make a Probability Distribution!!!!!

Probability Distribution of your Quiz Scores

x x 2x xx p(x) x·p(x) 2 ( )x x p x

0

12345

678

Mean, Variance, and Standard Deviation of a Probability Distribution

( )x x p x 2 ( )Variance x x p x

standard deviation = Variance