1. Chap 7.1 Discrete and Continuous Random Variables

2. Random Variable A variable taking numerical values determined by the outcome of a random phenomenon Usually represented by capital letters near the end of the alphabet (X, Y, Z)

3. Probability Distribution of a Random Variable (X) Tells us what the possible values of X are and how probabilities are assigned to those values.

4. Discrete Random Variable Has a finitely many possible values. All outcomes can be listed Each probability must be between 0 and 1 Sum of the probabilities is 1

5. Example 7.1 Getting good grades Stats 101, fall 2003, grade distribution: 21% A’s, 43% B’s, 30% C’s, 5% D’s, 1% F’s A student is chosen at random from this class (each student has the same probability of being chosen) Let X = student’s grade (A=4, B=3, C=2, D=1, F=0)

6. Probability distribution: Probability of getting a B or better? 0.64

7. Continuous Random Variable A variable in which values are not isolated numbers but an entire interval of numbers Variable takes on all values in an interval of numbers Cannot list all outcomes Probability distributions are described by a density curve Assign probability 0 to every individual outcome. No distinction between ≥ and >

8. Example 7.3 0.4 0.5 0.2 0.7

9. Normal Distribution

10. Example 7.4 Cheating in school

11. Assignment Pg. 469 1, 2, 7, 9, 14, 15