2. 6.1 Discrete Random Variables Objectives: By the end of this section, I will be able to… 1) Identify random variables. 2) Explain what a discrete probability distribution is and construct probability distribution tables and graphs. 3) Calculate the mean, variance, and standard deviation of a discrete random variable.

3. Making Decisions We are constantly making decisions. What should I wear today? What girl should I ask to the prom? Should I smoke that cigarette? One thing to do is to write out all the possible outcomes to a situation.

4. Random Variable A variable whose values are determined by chance. It must be RANDOM

5. TWO TYPES OF R.V. Continuous random variable When the random variable can take infinitely many values, usually an interval. Discrete random variable When the random variable can be counted or listed

6. Is it Discrete RV or Continuous RV? 1)Three cards are selected from a deck of cards. We want to know how many aces can be obtained. 2)Let x be the number of people who are going to attend Disney on Ice. 3)A nurse is taking your blood pressure. Let y be your systolic blood pressure. Discrete RV Continuous RV

7. Probability Distribution It is a table that shows the results of your experiment The SUM of the PROBABILITES must = 1 Random Variable, x p(x) 00.12 10.28 20.04 30.23 40.33 0.12 + 0.28 + 0.04 + 0.23 + 0.33 = 1.00

8. Probability Distribution How many siblings do you have? Random Variable, x p(x) 0 1 2 3 4 5 6

9. Probability Questions Answer the following using that chart: 1)p(x = 2) 2)p(x > 2) 3)p(x ≠ 4) 4)p(x ≤ 3) 5)p(not 1)

10. Mean, Variance, and Standard Deviation of a Probability Distribution

13. 1)This is the only animal that can’t jump. (Rhinoceros or an Elephant) 2)If Barbie were life-size she would be this tall. (6’0 or 7’2) 3)It is the shortest complete sentence in the English Language. (“No” or “Go”) 4)This part of your body never grows from birth. (Eyes or Brain)

14. 5) It is impossible to lead a cow upstairs or downstairs? 6) Which do people fear more, death or spiders? 7) Women do this nearly twice as much as men, shower or blink? 8) This animal is the slowest on Earth, tree sloth or tortoise

15. 1)This is the only animal that can’t jump. (Elephant) 2)If Barbie were life-size she would be this tall. (6’0) 3)It is the shortest complete sentence in the English Language. (“Go”) 4)This part of your body never grows from birth. (Eyes)

16. 5) It is impossible to lead a cows downstairs 6) Which do people fear more, spiders 7) Women do this nearly twice as much as men, blink 8) This animal is the slowest on Earth, tree sloth

17. What was your score? Let’s make a Probability Distribution!!!!!

18. Probability Distribution of your Quiz Scores xp(x)x·p(x) 0 1 2 3 4 5 6 7 8

19. Mean, Variance, and Standard Deviation of a Probability Distribution