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Discrete and Continuous Random Variables

Discrete and Continuous Random Variables. Chapter 7. Random Variables. A random variable is a variable whose value is a numerical outcome of a random event. Examples: Counting the number of eggs in a robin’s nest Measuring the daily rainfall in inches

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Discrete and Continuous Random Variables

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  1. Discrete and Continuous Random Variables Chapter 7

  2. Random Variables • A random variable is a variable whose value is a numerical outcome of a random event. • Examples: • Counting the number of eggs in a robin’s nest • Measuring the daily rainfall in inches • Counting the number of defective light bulbs that are in a case of light bulbs • Measuring the weight of a polar bear cub in kilograms.

  3. Defining a Random Variable • Let X = the number of wins the Huskies will have in a football season. • We say X is random variable because the outcomes of X are numerical values and are chance or random.

  4. Discrete Random Variable • When observations can have only a finite or countable number of outcomes. • Examples: • The number of students in a stats course. • The cost of tuition to the nearest cent.

  5. Continuous Random Variables • When observations can take on any of a countless number of values that you can measure. • Examples: • Tire pressure in cars • Heights of a group of students

  6. How can I tell the difference? • When you think of discrete random variables, think of counting the number of outcomes. • When you think of continuous random variables, think of things that you would measure like length, weight, volume, temperature or time.

  7. You make the call! • Time it takes to get ready in the morning. • The number of pages read a night. • The amount of gasoline in my gas tank.

  8. A discrete probability distribution Roll two dice - Let X = sum of the dice • What are the possible outcomes for X?

  9. Constructing a discrete probability distribution • P(X = 3) = _________ In English… • P(X < 3) = _________ • P(X ≤ 3) = _________

  10. Discrete Probability Histograms

  11. A CRV X takes all values in an interval of numbers Represent a CRV using a density curve Find probabilities for outcomes by finding the area under the density curve P(.3 < x < .7) = .4 P(X=0.3) = 0 Continuous Random Variables (CRV)Randomly generate a number between 0 and 1. How many possibilities are there?

  12. The End Homework: Exercises 7.12, 7.14, 7.17, 7.18

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