1. SWBAT: -Distinguish between discrete and continuous random variables -Construct a probability distribution and its graph -Determine if a distribution is a probability distribution -Calculate the mean, variance, and standard deviation of a discrete probability distribution -Calculate the expected value of a discrete probability distribution Agenda: -Notes -Homework

2. Probability Distributions Random Variable -A variable whose value is determined by the outcome of a random experiment Discrete Variable -A variable whose values are countable, no decimals or fractions 1, 2, 3, ….. Continuous Variable - A variable that can assume any numerical value Time, weight, height, etc…

3. Example: Determine whether the random variable is Discrete or Continuous -Time taken to complete an exam -Continuous -Number of houses on a block -Discrete -The weight of a newborn child -Continuous -The price of a house -Continuous

4. Discrete Probability Distribution Lists all possible values that a random variable can assume and their corresponding probabilities The following conditions must be met: - each probability must be between or equal to 0 and 1 0 ≤ P(x) ≤ 1 - sum of all probabilities equal 1 ∑ P(x) = 1 Number of Vehicles Owned Probability 1.241 2.439 3.293 4.027 Variable x - each between 0 and 1 - add up to 1

5. Example: The following table represents the number of students in a class with a certain eye color. Eye ColorFrequency Brown13 Blue9 Green5 Hazel3 Construct a probability distribution table and graph using a histogram. Note: the area under each bar in histogram represents the probability of that category

6. Mean – of a discrete random variable µ = ∑ x P(x) Variance – of a discrete random variable σ 2 = ∑ (x - µ) 2 P(x) ** In order to do this on the calculator, enter the values of x in L 1 and the probabilities in L 2. Use 1- Variable Statistics to find mean and standard deviation.

7. Example: Find the mean, variance and standard deviation for the following probability distributions XP(x) 6.40 7.26 8.21 9.13 µ = 7.07 σ = 1.06 σ 2 = 1.12

8. Expected Value - the result you would expect to happen if the experiment was repeated thousands of times - is equal to the mean of the discrete random variable Expected Value = E(x) = Ʃ xP(x) Example: If 5000 raffle tickets are sold for $5 each and the cash payouts are $5000, $3000, $2000, and $1000. If you buy one ticket, what is your expected gain?

9. Homework Pg 197 #14 -44 even