Class Notes 7 - 6.1 How Can We Summarize Possible Outcomes...

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6.1 How Can We Summarize Possible Outcomes and Their Probabilities? Random Variable – its value is a numerical outcome of a random phenomenon. We use letters such as X and Y to denote a RV. Examples: Toss a coin 10 times, record number of heads. Roll two dice, record the sum Ask 100 people if they approve of the president, record the number of “yes” answers. Count number of defective items in a production line. Record scores on an exam for each student. Measure the height, weight, age, or GPA of college students. Discrete: a random variable is discrete if its set of possible values is a collection of isolated points on the number line. Continuous: a random variable is continuous if its set of possible values includes an entire interval on the number line. We will use lowercase letters, such as x and y, to represent random variables. 1. Experiment: A fair die is rolled Random Variable: The number on the up face Type: 2. Experiment: A pair of fair dice are rolled Random Variable: The sum of the up faces Type: 3. Experiment: A coin is tossed until the 1st head turns up Random Variable: The number of the toss that the 1st head turns up Type: 4. Experiment: Choose and inspect a number of parts Random Variable: The number of defective parts Type: 5. Experiment: Measure the voltage in a outlet in your room Random Variable: The voltage Type: 6. Experiment: Observe the amount of time it takes a bank teller to serve a customer Random Variable: The time Type: 7. Experiment: Measure the time until the next customer arrives at a customer service window Random Variable: The time Type: Possible values of a discrete random variable Possible values of a continuous random variable
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8. Experiment: Inspect a randomly chosen circuit board from a production line Random Variable: 1, if the circuit board is defective 0, if the circuit board is not defective Type: Probability Distributions for Discrete Random Variables A discrete RV has a finite list of possible outcomes. The probability distribution of a discrete random variable specifies all the values of X and their probabilities. The probabilities must satisfy the following two properties: Every probability P(x) falls between 0 and 1. All the probabilities add up to one. We can make a probability histogram to show the probability distribution of a discrete random variable. Example: Grades on a very large statistics class are given according to the following distribution: A B C D F 15% 35% 30% 16% 4% a) Define the random variable X as the number of grade points given for each grade. Write the probability distribution of X. X P(X) b) Is this a legitimate probability distribution? c)
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This note was uploaded on 04/21/2008 for the course MATH 220 taught by Professor Ruffin during the Fall '07 term at James Madison University.

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Class Notes 7 - 6.1 How Can We Summarize Possible Outcomes...

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