1. Objective: Objective: Use experimental and theoretical distributions to make judgments about the likelihood of various outcomes in uncertain situations CHS Statistics

2.   Decide if the following random variable x is discrete(D) or continuous(C). 1)X represents the number of eggs a hen lays in a day. 2)X represents the amount of milk a cow produces in one day. 3)X represents the measure of voltage for a smoke-detector battery. 4)X represents the number of patrons attending a rock concert. Warm-Up

3.   Random variable - A variable, usually denoted as x, that has a single numerical value, determined by chance, for each outcome of a procedure.  Probability distribution – a graph, table, or formula that gives the probability for each value of the random variable. Random Variable X

4.   A study consists of randomly selecting 14 newborn babies and counting the number of girls. If we assume that boys and girls are equally likely and we let x = the number of girls among 14 babies…  What is the random variable?  What are the possible values of the random variable (x)?  What is the probability distribution? Random Variable X

5.   A discrete random variable has either a finite number of values or a countable number of values.  A continuous random variable has infinitely many values, and those values can be associated with measurements on a continuous scale in such a ways that there are no gaps or interruptions.  Usually has units Types of Random Variables

6.   A Discrete probability distribution lists each possible random variable value with its corresponding probability.  Requirements for a Probability Distribution: 1.All of the probabilities must be between 0 and 1.  0 ≤ P(x) ≤ 1 2.The sum of the probabilities must equal 1.  ∑ P(x) = 1 Discrete Probability Distributions

7.   The following table represents a probability distribution. What is the missing value? Discrete Probability Distributions (cont.) x12345 P(x) 0.160.220.280.2

8.   Do the following tables represent discrete probability distributions? 1)2)3) 4) Discrete Probability Distributions (cont.) xP(x) 0 0.216 2 0.432 3 0.288 4 0.064 xP(x) 5 0.28 6 0.21 7 0.43 8 0.15 xP(x) 1 1/2 2 1/4 3 5/4 4 xP(x) 1.09 2 0.36 3 0.49 4 0.06 5) P(x) = x/5, where x can be 0,1,2,3 6) P(x) = x/3, where x can be 0,1,2

9.  Mean and Standard Deviation of a Probability Distribution Very important!

10.   Calculate the mean and standard deviation of the following probability distributions: Mean and Standard Deviation of a Probability Distribution (cont.) 1) Let x represent the # of games required to complete the World Series: 2) Let x represent the # dogs per household:

11.  Expected Value

12.   Consider the numbers game, often called “Pick Three” started many years ago by organized crime groups and now run legally by many governments. To play, you place a bet that the three-digit number of your choice will be the winning number selected. The typical winning payoff is 499 to 1, meaning for every $1 bet, you can expect to win $500. This leaves you with a net profit of $499. Suppose that you bet $1 on the number 327. What is your expected value of gain or loss? What does this mean? Expected Value

13.   pp. 190 # 2 – 14 Even, 18 – 22 Even Assignment