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chap11_2010 - Chapter 11 Discrete Random Variables and...

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Chapter 11 Discrete Random Variables and their Probability Distributions
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Random Variables A random variable is a numerical outcome of a random experiment A discrete random variable can take on only specific, isolated numerical values, Finite discrete random variables: Discrete random variables that can take on only finitely many values (like the outcome of a roll of a die) Infinite discrete random variables: Discrete random variables that can take on an unlimited number of values (like the number of stars estimated to be in the universe) A continuous random variable can take on any values within a continuous range or an interval (like the temperature, or the height of an athlete in centimeters.)
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Random Variables Example Experiment: Next four customers who enter a bank Random variable x: the number of customers who make a deposit (D) x = 1 represents the event “exactly one customer makes a deposit” x Outcomes 0 NNNN 1 DNNN,NDNN,NNDN,NNND 2 DDNN,DNDN,DNND,NDDN,NDND,NNDD 3 DDDN,DDND,DNDD,NDDD 4 DDDD D represents a customer who makes a deposit, N represents a customer who does not.
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Discrete vs. Continuous Random Variables DISCRETE CONTINUOUS Values that can be counted and ordered Values that cannot be counted Gap between consecutive values On continuous spectrum Examples: 1) Insurance claims filed in one day 2) Cars sold in one month 3) Employees who call in sick on a day Examples: 1) Time to check out a customer 2) Weight of an outgoing shipment 3) Distance traveled by a truck in a single day 4) Price of a gallon of gas Measure with a specific amount of precision
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Probability Distributions of a Discrete Random Variable The distribution of a random variable is the collection of possible outcomes along with their probabilities. This may be described by a table, a formula, or a probability histogram. The probability assigned to each value of x lies in the range 0-1. The sum of all the probabilities of x must equal 1. 1 ) ( 0 x P = 1 ) ( x P
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Probability Distributions of a Discrete Random Variable: Example The probability distribution of x describes a list of all the possible values that a x can assume and their corresponding probabilities. CALCULATE the probability of : P(Exactly one depositor in four customers) or P(x=1) P(two or more depositors) or P(x2) P(Fewer than four depositors) or (P(x<4) x Outcomes P( X) 0 NNNN 1/16 = .0625 1 DNNN, NDNN, NNDN, NNND 4/16 = .2500 2 DDNN, DNDN, DNND, NDDN, NDND, NNDD 6/16 = .3750 3 DDDN, DDND, DNDD, NDDD 4/16 = .2500 4 DDDD 1/16 = .0625
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Mean of a Discrete Random Variable The mean of a discrete random variable, μ , is actually the mean of its probability distribution. The mean is also called the expected value
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chap11_2010 - Chapter 11 Discrete Random Variables and...

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