311_session_5.5_probability

311_session_5.5_probability - Probability Concepts BUAD311...

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1 Probability Concepts BUAD311 Operations Management Session 5.5
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2 Random Experiment Random Experiment: An experiment in which the precise outcome is not known ahead of time. The set of possibilities is known. Examples: Demand for iPhones next month GM stock price tomorrow The waiting times of customers in the bank Tomorrow’s closing value of the NASDAQ The temperature in Los Angeles tomorrow
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3 Random Variable A random variable is the numerical value determined by the outcome of a random experiment A random variable can be discrete (i.e. takes on only a finite set of values) or continuous Examples: The value on a rolled die is a discrete random variable The demand for iPhones is a discrete random variable The birth weight of a newborn baby is a continuous variable The waiting time for the AT&T service person is a
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4 Sample Space Sample space is the list of possible outcomes of an experiment Examples: For a die, the sample space S is: {1,2,3,4,5,6} For the demand for blue blazers it is all possible realizations of the demand. For example: {1000,1001,1002…,2000} The waiting time in the bank is any number greater than or equal to 0. This is a continuous random variable The waiting time for a bus at a bus stop is any number between 0 and 30 minutes. This is a continuous random variable that is bounded
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5 Event An event is a set of one or more outcomes of a random experiment Examples: Getting less than 5 by rolling the die: This event occurs if the values observed are {1,2,3, or 4} The demand is smaller or equal to 1500. This event occurs if the values of the demand are {1000, 1001, … 1500} The waiting time for a bus at the bus stop exceeds 10. This event occurs if the wait time is in the interval (10, 30)
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6 Probability The probability of an event is a number between 0 and 1 1 means that the event will always happen 0 means that the event will never happen The probability of an event A is denoted as either P(A) or Prob(A)
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7 Probability If all the outcomes that constitute the sample space are equally likely, then the probability of an event A is: P(A) = (Number of outcomes that result in event A) / (number of possible outcomes) Example: Probability of rolling a die and observing a number less than 5 = P(outcome< 5) = Prob(observing
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8 Probability Probability that A doesn’t occur: P(not A) = 1 – P(A) Thus, the probability you will roll a number larger or equal to 5 is or 6 is: 1 – Probability (Outcome <5) = 1 – 2/3 = 1/3
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Probability Suppose all the outcomes that constitute the “waiting time” for an AT&T operator are equally likely . The minimum waiting time is 30 min and the maximum is 90 min. Then the probability of waiting
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311_session_5.5_probability - Probability Concepts BUAD311...

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