Transcript powerpoint

6.1 Discrete Random Variables
Objectives:
By the end of this section, I will be
able to…
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.
1)
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. Discrete RV
2) Let x be the number of people who are
going to attend Disney on Ice. Discrete RV
3) A nurse is taking your blood pressure.
Let y be your systolic blood pressure.
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
0
1
2
3
4
p(x)
0.12
0.28
0.04
0.23
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
0
1
2
3
4
5
6
p(x)
Probability Questions
•
Answer the following using that chart:
1)
2)
3)
4)
5)
p(x = 2)
p(x > 2)
p(x ≠ 4)
p(x ≤ 3)
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)
Variance    x  x   p ( x)
2
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
0
1
2
3
4
5
6
7
8
p(x)
x·p(x)
xx
x  x
2
x  x
2
 p( x)
Mean, Variance, and Standard
Deviation of a Probability Distribution
x   x  p ( x)
Variance    x  x   p ( x)
2
standard deviation = Variance