modelling using Random Variables . . . . . . . . . . . . 2 Lecture 2. Random variables. Revision. 2.1 Random Variables and Their Distributions. General. . . . 2.2 Expected value= mean‚ Variance=( Standard Deviation)2 . 2.3 Common models. Specific Probability distributions. . . . . 2.4 Realization of Random Variables. Using Excel . . . . . . . 2.5 Expectation of a function of a random variable . . . . . . . 3 Lecture 3. Multivariate distributions. 3.1 Independence . . . . . . . . . . . . . . 3.2 Covariance
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decision tree we know that the decision to develop thoroughly has a probability of 0.4 in a good market and predicted gains of $500‚000. The second State of nature would be a moderate market reaction with a probability of .4 and predicted gains of $25‚000. The third state of nature is a poor market reaction with a probability of .2 with predicted gains of $1‚000. The expected monetary value (EMV) is determined by multiplying the probability in each state of nature by the predicted gains and then adding
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line. Erlang (a Danish Telephone engineer) began a study of congestion and waiting times in the completion of telephone calls. Operating Characteristic (performance Measure) for a waiting Line Model Probability that no units are in the system Probability that an arriving unit has to wait for service Average Number of units in waiting line or system Average Time a unit spends in waiting line or system Make a decision that balance desirable service level against the
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outcomes is called a(n) sample space. event. experiment. probability. 3. Question : If two events are independent‚ then the probability of their intersection is represented by: P(A ? B) = P(A) + P(B) P(A ? B) = 0 P(A ? B) = P(A) * P(B) P(A ? B) = P(A) - P(B) P(A ? B) = P(A) * P(A | B) 4. Question : A(n) __________ is a measure of the chance that an uncertain event will occur. experiment sample space probability complement population 5. Question : The price-to-earning
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15 percent probability of a boom‚ a 75 percent chance of a normal economy‚ and a 10 percent chance of a recession. What is your expected rate of return on this stock? a. 5.00 percent b. 6.45 percent c. 7.30 percent d. 7.65 percent e. 8.30 percent EXPECTED RETURN a 61. The Inferior Goods Co. stock is expected to earn 14 percent in a recession‚ 6 percent in a normal economy‚ and lose 4 percent in a booming economy. The probability of a boom is
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Analyzing Waiting Lines Most people find waiting lines irritating – waiting is idle and nonproductive time. From a service system perspective‚ however‚ a line represents a demand for service. Think of a restaurant on a Friday night. As a customer it is an irritation to have to wait 40 plus minutes for a table‚ but from the restaurant’s perspective‚ if there is not a line‚ then that means there are empty tables. Idle services are not good. So management must balance waiting time with the
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examined. These areas are that of structural components‚ alternative program characteristics and ways to evaluate the program. All of the aforementioned areas will be examined in this paper‚ in relation to a local Social Welfare program - The Targeted Conditional Cash Transfer Programme. Structural Components Dolgoff and Feldstein highlight five (5) key structural characteristics that are needed for examination of a social welfare programme to occur. The key characteristics that will be systematically
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The time at which the mailman delivers the mail follows a normal distribution with a mean of 2:00PM and a standard deviation of 15 minutes (20 pts) a) What is the probability that the mail will arrive before 1:50PM? b) What is the probability that the mail will arrive after 2:30PM? c) What is the probability that the mail will arrive between 1:40PM and 2:20PM? d) Between what two times (equally before the mean and equally after the mean) accounts for the mail being delivered
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DISTRIBUTIONS I. Concept of probability (3%) 1. Explain why the distribution B(n‚p) can be approximated by Poisson distribution with parameter if n tends to infinity‚ p 0‚ and = np can be considered constant. 2. Show that – and + are the turning points in the graph of the p.d.f. of normal distribution with mean and standard deviation . 3. What is the relationship between exponential distribution and Poisson distribution? II. Computation of probability (7%) 1. Let
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Decision tree for Friday pressing Mr. Ward is trying to decide on how many CDs to press on the first night of the festival. His intuition combined with his experience allowed him to make some predictions of demand. These take the form of probabilities. “The probabilities may be subjective estimates from managers or from experts in a particular field‚ or they may reflect historical frequencies. If they are reasonably correct‚ they provide a decision maker with additional information that can dramatically
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