LEARNING TARGETS
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use a probability distribution to answer questions about possible values of a
random variable.
calculate the mean and standard deviation of a discrete random variable.
interpret the mean and standard deviation of a random variable.
describe the effects of transforming a random variable by adding or
subtracting a constant and multiplying or dividing by a constant.
find the mean and standard deviation of the sum or difference of
independent random variables.
determine whether two random variables are independent.
find probabilities involving the sum or difference of independent Normal
random variables.
determine whether the conditions for a binomial random variable are met.
calculate the mean and standard deviation of a binomial random variable
and interpret these values in context.
compute and interpret probabilities involving binomial distributions.
find probabilities involving geometric random variables.
determine whether the conditions for the Normal approximation to a
binomial distribution are met. When appropriate, use the Normal
approximation to estimate probabilities in a binomial setting.
WHAT SHOULD WE DO/KEEP?
WHAT SHOULD WE CHANGE?
UNIT 6 – CHAPTER 6
6.1 – Discrete and Continuous Random Variables
DO YOU REMEMBER?
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What is a probability distribution?
DEFINITIONS
A random variable takes numerical values that
describes the outcomes of some chance process.
 The probability distribution of a random
variable gives its possible values and their
probabilities.
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DISCRETE RANDOM VARIABLE
A discrete random variable X takes a fixed set
of possible values with gaps between.
 For example: grades on the AP test
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(0, 1, 2, 3, 4 ,5)
EXPECTED VALUE (MEAN)
The mean 𝜇𝑥 of a discrete random variable X is
also an average of the possible values of X.
 To find the mean (expected value) of X,
multiply each possible value by its probability
then add all of the products.
 For example – Winning at Roulette
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Value
-$1
$1
Probability
20/38
18/38
APGAR SCORES
Dr. Apgar suggested five criteria for measuring a
baby’s health at birth: skin color, heart rate,
muscle tone, breathing, and response with
stimulated (each scored 0-1-2).
 Why are these discrete?
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Value
0
1
2
3
4
5
6
7
8
9
10
Prob.
.001
.006
.007
.008
.012
.020
.038
.099
.319
.437
.053
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Find the expected value.
STANDARD DEVIATION (AND VARIANCE)
OF A DISCRETE RANDOM VARIABLE
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When you use the mean (expected value) you will
also use the standard deviation. No surprise!
Variance:
Standard Deviation is the square root of the
variance.
APGAR SCORES: HOW VARIABLE ARE THEY?
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Compute and interpret the standard deviation:
Value
0
1
2
3
4
5
6
7
8
9
10
Prob.
.001
.006
.007
.008
.012
.020
.038
.099
.319
.437
.053
CONTINUOUS RANDOM VARIABLE
A continuous random variable X takes all values
in an interval of numbers. The probability
distribution of X is described by a density curve.
The probability of any event is the area under the
density curve and above the values of X that
make up the event.
 For example – heights of all people in this room
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YOU DECIDE! DISCRETE OR CONTINUOUS?
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Time it takes you to clean your room
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How much it costs for dinner
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Inches of rainfall last month
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Your birthday
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The outcome of the roll of a dice
HOMEWORK
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P. 353 (2-8 even, 9, 12-18 even, 21-30)