1. 6.1 Probability Distribution
Pg. 212

2. Background Vocabulary
Random Variable
A variable whose value is determined by the outcomes of a random event
Discrete Random Variable
A variable that can take on only a countable number of distinct values
Continuous Random Variable
A variable that can take on an uncountable, infinite number of possible values, often over a specified interval
Probability Distribution
A function that gives the probability of each possible value of a random variable. The sum of all the probabilities in a probability distribution must equal 1.

3. Background Vocabulary (cont)
Binomial Distribution
Shows the probabilities of the outcomes of a binomial experiment
Binomial (success and failure)
Binomial Experiment
Has n independent trials, with two possible outcomes (success or failure) for each trial. The probability for success is the same for each trial. The probability of exactly k successes in n trials is …
Symmetric Distribution
If a vertical line can be drawn to divide the histogram of the distribution into two parts that are mirror images
Skewed
If a distribution is not symmetric it is skewed

4. 6 x 6 = 36 in the sample space Sample space for 2 Dice 11 21 31 41 5161 12 22 32 42 52 62 13 23 33 43 53 63 14 24 34 44 54 64 15 25 35 45 55 65 16 26 36 46 56 66 11 21 31 41 51 61 12 22 32 42 52 62 13 23 33 43 53 63 14 24 34 44 54 64 15 25 35 45 55 65 16 26 36 46 56 66
6 x 6 = 36 in the sample space

5. Indicate the number of ways you can get a sum of the following with 2 dice.
Frequency
Theoretical Probability 2 3 4 5 6 7 8 9 10 11 12 11 21 31 41 51 61 12 22 32 42 52 62 13 23 33 43 53 63 14 24 34 44 54 64 15 25 35 45 55 65 16 26 36 46 56 66 1 2

6. Make a Probability Histogram
Indicate the number of ways you can get a sum of the following with 2 dice.
Make a Probability Histogram
.18
.16
.14
.12
.10 .8 .6 .4 .2
Sum
Frequency
Theoretical Probability 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 5 4 3 2 1

7. Probability of the # of Cell Phones/Household
Guided Practice #1
Page 213
Probability of the # of Cell Phones/Household
Dependent Variable
Independent Variable

8. Guided Practice #1
Page 213

9. Binomial
Distribution
Success
Failure

10. In a standard deck of cards, 25% are spades
In a standard deck of cards, 25% are spades. Suppose you choose a card at random, note it is a spade, then replace it. You conduct the experiment 3 times. Draw a histogram of the binomial distribution for your experiment.
n =
k =
p =
1 – p =
P(k=0) =
P(k=1) =
P(k=2) =
P(k=3)=

11. Calculator Short Cuts binompdf-
Binomial Probability Distribution Function
Used for the probability of k successes in n trials
Type 2nd, VARS (DISTR), Down to
binompdf(n,p,k)
Example (3 – trials, success = 30%, 2 successes)
Exactly 2 successes in 3 trials w/ 30% success
can be used instead of

12. Calculator Short Cuts binomcdf-
Binomial Cumulative Distribution Function
Used for the sum of the probabilities of k successes in n trials
Type 2nd, VARS (DISTR), Down to
binomcdf(n,p,k)
Example (3 – trials, success = 30%, k ≤ 2)
0, 1, or 2 successes in 3 trials w/ 30% success
This only works for 0 to the amount of successes needed, if the problem was for greater than, just use the compliment, (1 – (P))

13. n = k = p = 1 – p = P(k=0) = P(k=1) = P(k=2) = P(k=3) = P(k=4) =
Guided Practice #4-6
Page 214
n =
k =
p =
1 – p =
P(k=0) =
P(k=1) =
P(k=2) =
P(k=3) =
P(k=4) =
Discuss #5 and 6

14. n = k = p = 1 – p = P(k=0) = P(k=1) = P(k=2) = P(k=3) = P(k=4) =
Guided Practice #4-6
Page 214
n =
k =
p =
1 – p =
P(k=0) =
P(k=1) =
P(k=2) =
P(k=3) =
P(k=4) =
Discuss #5 and 6

15. Homework
Pg. 215, 1 – 15 odds
Pg. 216, odds