1. 10-3 Probability distributions
Day 1

2. I can construct a probability distribution.
Objective
I can construct a probability distribution.
I can analyze a probability distribution and its summary statistics.

3. Discrete Vs. Continuous
A sample space is the set of all possible outcomes in a distribution. Consider a distribution of values represented by the sum of the values on two dice and a distribution of the miles per gallon for a sample of cars.

4. Random Variable
The value of a random variable is the numerical outcome of a random event. A random variable can be discrete or continuous. Discrete random variables represent countable values. Continuous random variables can take on any value.

5. Example 1
Identify the random variable in each distribution, and classify it as discrete or continuous. Explain your reasoning.
The number of songs found on a random selection of mp3 players
The weights of football helmets sent by a manufacturer
The ages of counselors at a summer camp

6. Probability Distribution
A theoretical probability distribution is based on what is expected to happen. For example, the distribution for flipping a fair coin is P(heads) = 0.5, P(tails) = 0.5.
An experimental probability distribution is a distribution of probabilities estimated from experiments. When using this type of distribution, use the frequency of occurrences of each observed value to compute its probability.

7. X represents the sum of the values on two dice.
Example 2
X represents the sum of the values on two dice.
Construct a relative-frequency table.
Graph the theoretical probability distribution.

8. X represents the sum of the values of two spins of the wheel.
Example 3
X represents the sum of the values of two spins of the wheel.
Construct a relative-frequency table.
Graph the theoretical probability distribution.

9. 10-3 Probability distributions
Day 2

10. Expected Value
Probability distributions are often used to analyze financial data. The two most common statistics used to analyze a discrete probability distribution are the mean, or expected value, and the standard deviation. The expected value E(X) of a discrete random variable of a probability distribution is the weighted average of the variable.

11. Expected value

12. Example 1
A game-show contestant has won one spin of the wheel at the right. Find the expected value of his winnings.

13. Example 2
Curt won a ticket for a prize. The distribution of the values of the tickets and their relative frequencies are shown. Find the expected value of his winnings.

14. Standard Deviation of a probability distribution

15. Example 3
Jimmy is thinking about investing $10,000 in two different investment funds. The expected rates of return and the corresponding probabilities for each fund are listed below.

16. Example 3 cont.
Find the expected value of each investment.
Find each standard deviation.
Which investment would you advise Jimmy to choose, and why?

17. Example 4
Compare a $10,000 investment in the two funds. Which investment would you recommend, and why?