Chap_6 - Chapter 6 Discrete Probability Distribution...

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Unformatted text preview: Chapter 6 Discrete Probability Distribution Chapter Goals After completing this chapter, you should be able to:  Understand the discrete random variables and there probability distribution.  Compute the expected value and standard deviation for a discrete probability distribution  Apply the binomial distribution to applied problems Introduction to Probability Distributions  Random Variable  Represents a possible numerical value from a random event Random Variables Discrete Random Variable Continuous Random Variable  A discrete random variable is a variable that can assume only a countable number of values Many possible outcomes:  number of complaints per day  number of TV‟s in a household  number of rings before the phone is answered Only two possible outcomes:  gender: male or female  defective: yes or no  spreads peanut butter first vs. spreads jelly first Discrete Probability Distributions Discrete Random Variables  Can only assume a countable number of values Examples:  Roll a die twice Let x be the number of times 4 comes up (then x could be 0, 1, or 2 times)  Toss a coin 5 times. Let x be the number of heads (then x = 0, 1, 2, 3, 4, or 5) Experiment: Toss 2 Coins. Let x = # heads. T T Discrete Probability Distribution 4 possible outcomes T T H H H H Probability Distribution 0 1 2 x x Value Probability 0 1/4 = .25 1 2/4 = .50 2 1/4 = .25 .50 .25 Probability  A list of all possible [ x i , P(x i ) ] pairs x i = Value of Random Variable (Outcome) P(x i ) = Probability Associated with Value  x i ‟s are mutually exclusive (no overlap)  x i ‟s are collectively exhaustive (nothing left out)  0  P(x i )  1 for each x i  S P(x i ) = 1 Discrete Probability Distribution Discrete Random Variable...
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This note was uploaded on 03/22/2012 for the course FINA 210 taught by Professor Dakroub during the Spring '12 term at American University in Cairo.

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Chap_6 - Chapter 6 Discrete Probability Distribution...

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