Announcements
Finite Probability
Monday, October 31st
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MyMathLab 7 is due Wednesday Nov 2
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Problem Set 7 is due Friday Nov 4
Today: Sec. 7.2: Frequency Distributions
Understand the difference between a relative frequency
distribution and a probability distribution
Create a probability distribution for a random variable
Next Class: Sec. 7.3: Binomial Trials
Cherveny
Oct 31
Math 1004: Probability
Frequency vs Relative Frequency
Definition
Suppose you perform a probability experiment n times.
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The frequency of an outcome is the number of times it
occurred.
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The relative frequency of an outcome is the number of times
it occurred divided by n.
Cherveny
Oct 31
Math 1004: Probability
Flipping a Coin
Example
Each person in the class flips a coin 7 times and observe the
number of heads flipped.
Make a frequency distribution and a relative frequency distribution
of the class results. Also make a histogram to visualize these.
Cherveny
Oct 31
Math 1004: Probability
Flipping a Coin
Example
Instead of actually tossing a coin 7 times, make a probability
distribution for the theoretical relative frequency of each outcome.
That is, let X denote the possible outcomes, i.e. X = 0, 1, . . . , 7.
What is the probability of each of these?
Let k be the number of heads flipped in 7 times. Can you find a
function for the probability of getting k heads?
Cherveny
Oct 31
Math 1004: Probability
Flipping a Coin
Let X be the number of heads flipped in 7 times. Can you find a
function for the probability of getting X = k heads?
Answer: P(X = k) =
Cherveny
C (7,k)
27
Oct 31
Math 1004: Probability
Flipping a Coin
Now we’ll flip the coin until you get heads for the first time. What
does the class histogram fro relative frequencies look like?
Also, let X be the number of flips until the first heads. Can you
find a function for the probability of getting X = k?
k
Answer: P(X = k) = 12
Cherveny
Oct 31
Math 1004: Probability
Random Variables
Definition
A random variable X is a numerical observation made on a
probability experiment.
Example
When flipping a coin 7 times, X counting the number of heads is a
random variable.
Cherveny
Oct 31
Math 1004: Probability
Random Variable or Not
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Flip a coin seven times. Let X be the sequence of outcomes.
Answer: Not a random variable.
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Roll a fair die. Let X be the square of the roll minus 10.
Answer: Random variable.
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Roll a die twice, win $2 for each 3 and lose $1 for any other
roll. Let X be your winnings.
Answer: Random variable.
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Pick a random person on campus. Let X be their age plus
weight.
Answer: Random variable.
Cherveny
Oct 31
Math 1004: Probability
Practice
1. An archer can hit the bull’s-eye of the target with probability
1/3. She shoots until she hits the bull’s-eye or until three
shots have been taken. The number of shots is observed.
Define a random variable for the experiment and find its
probability distribution.
2. Let Y be the random variable with probability distribution
given below. Determine the probability distributions for the
random variables Y 2 and Y + 2.
k
−2
−1
0
1
2
3
Cherveny
Oct 31
P(Y = k)
.2
.1
.12
.25
.15
.18
Math 1004: Probability