311_session_5_Probability

# 311_session_5_Probability - Probability Concepts BUAD311...

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1 Probability Concepts BUAD311 Operations Management Session 5

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2 Quote of the day “Without the element of uncertainty, the bringing off of even the greatest business triumph would be dull, routine, and eminently unsatisfying.” -J. Paul Getty
3 Decision Making Under Uncertainty DR Horton Should you start developing now? Noah’s Bagel How many bagels do you want to bake this morning? Netflix How many copies of “The Time Traveler’s Wife” do you want to buy from the studio? CBS What is the right price for a 2 minute ad

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Probability To answer and communicate these questions effectively, we need the language of probability. 4
5 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 The waiting time for an AT&T service person Tomorrow’s closing value of the NASDAQ The temperature in Los Angeles tomorrow

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6 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
7 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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8 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)
9 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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10 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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