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CHAPTER 5: Discrete Probability Distributions

CHAPTER 5: Discrete Probability Distributions. 5.1 Probability Distributions. Random Variables. A random variable is a variable whose value is a numerical outcome of a random phenomenon. let X = number of heads. if we get HHTH, X = 3 if we get TTTH, X = 1

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CHAPTER 5: Discrete Probability Distributions

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  1. CHAPTER 5:Discrete Probability Distributions 5.1 Probability Distributions

  2. Random Variables A random variable is a variable whose value is a numerical outcome of a random phenomenon. • let X = number of heads. • if we get HHTH, X = 3 • if we get TTTH, X = 1 • What is the sample space for X?

  3. Random Variables • they are variables because they keep changing • they are random because we don’t know the next value the variable will assume. • we DO know the overall pattern of the values assumed by a random variable over many repetitions.

  4. Random Variables • A discrete random variable has a countable number of possible values. • usually counts

  5. ounces Random Variables • A continuous random variable can take any value in an interval of the real number line. • usually measurements

  6. DISCRETE orCONTINUOUS? • weight of a book • number of chapters in a book • number of defects in a square yard of fabric • number of homeruns in a season • weight of a boat-load of fish

  7. DISCRETE Random Variables • We will use capital letters to represent discrete random variables • usually X or Y • corresponding lower case letters will represent values of the random variable. • P(X = x) is the probability that the random variable X equals the value x.

  8. DISCRETE Random Variables • the probability distribution of Xlists the values and their probabilities. • Every piis between 0 and 1. • the sum of the p’s is 1.

  9. DISCRETE Random Variables • Find the probability distribution for a gender for a family with three single births. • Express P(at least two boys) in terms of X. • find it.

  10. DISCRETE Random Variables • Create a Probability Distribution for rolling a six sided die.

  11. DISCRETE Random Variables • 25% of women cannot distinguish between the colors red and green. • Find the probability distribution for 3 randomly chosen women. • So, what is the probability that exactly two women will be colorblind? • What is the probability that at least one will not be colorblind?

  12. DISCRETE Random Variables Create a Probability Distribution for the following: The probabilities of a return on an investment of 1000, 2000, 3000 are ½, ¼, and ¼ respectively.

  13. DISCRETE Random Variables Create a Probability Distribution for the following: A die is weighted so that the probabilities of getting 1, 2, 3, 4, 5, and 6 are ½, 1/6, 1/12, 1/12, 1/12, and 1/12 respectively.

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