generate random numbers. In the Monte Carlo process, values for a random variable are generated by sampling from a probability distribution. We will transfer the ranges of random numbers for each Repair time value to a table Repair Time,y | Probability of repair time | Cumulative probablility | Ranges of Random number | 1 | 0.20 | 0.2 | 0-0.2 | 2 | 0.45 | 0.65 | 0.21-0.65 | 3 | 0.25 | 0.9 | 0.66-0.9 | 4 | 0.10 | 1.0 | 0.91-1.0 | We use the function =Rand() in excel to generate random numbers
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Mathematical Conventions for the Quantitative Reasoning Measure of the GRE® revised General Test www.ets.org Overview The mathematical symbols and terminology used in the Quantitative Reasoning measure of the test are conventional at the high school level, and most of these appear in the Math Review. Whenever nonstandard or special notation or terminology is used in a test question, it is explicitly introduced in the question. However, there are some particular assumptions about numbers
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US Public Health Service (PS-1) Group 8, Section C Background Information: The existing procedure for detecting syphilitic men was to subject each person to the Wasserman-type blood test. The alternative method suggests blood sera be drawn from groups of people, and the groups should be subjected to chemical analysis. If the group test reveals the presence of antigen, the individual blood samples would be tested to identify the person. Assumptions 1. The event of one person testing
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examples and end of section exercises that can be used as a guide. Be sure to show your work in case partial credit is awarded. To receive full credit, work must be shown if applicable. Section 4.1 Probability Distribution 1. Decide whether the random variable is discrete or continuous. (References: example 1 page 195, end of section exercises 13 – 20 page 201) (1 point per each part) a. The cost of a randomly selected apple Discrete b. The height of randomly selected
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Joint Probability Distributions Example: Let X and Y be jointly continuous random variables having joint density f (x, y) = 3y 0 for 0 ≤ x ≤ y ≤ 1, otherwise. Sketch the domain of f as well as f . T E © Determine P (Y ≤ 2X). 1 Jointly Discrete Probability Distributions Definition 5.1: Let X and Y be discrete random variables. The joint probability mass function of X and Y is p(x, y) = P (X = x, Y = y) which is defined for all x and y. Remark: The joint distribution can
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the RAND() function in Excel to produce random values for column B9:B22. Once the RAND() function produced values, I copied and pasted just the values in column B9:B22 (to ensure the values would stay frozen and not continue to change). Once I had the random probabilities, I used the table given with the case (entered in cells A1:C6) to find the number of days need to repair. To find this information I used Excel function VLOOKUP, which matched the random probability to the cumulative probability
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1 a) The graph of the probability distribution of X is shown below: 1 b) As the sum of the probabilities of all expectations equals to 1 (0.108+0.562+0.33+0=1), X is a random variable. 1 c&d)The expected value, variance and standard deviation of X are calculated as follows: Interest rate, xi (%) Probability, Pr Pr * xi(%) Pr * (xi-E(X))^2 1.75 0.000 0.0000 0.00000 2 0.330 0.6600 0.01248 2.25 0.562 1.2645 0.00173 2.5 0.108 0.2700 0.01008 Expected value of X, E(X) 2.1945
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Assignment #1: JET Copies Case Problem Read the “JET Copies” Case Problem on pages 678-679 of the text. Using simulation estimate the loss of revenue due to copier breakdown for one year, as follows: 1. In Excel, use a suitable method for generating the number of days needed to repair the copier, when it is out of service, according to the discrete distribution shown. 2. In Excel, use a suitable method for simulating the interval between successive breakdowns, according to the continuous
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flood, fire, tornado, being held legally liable for damage to someone else and a host of other causes of loss. UNDERSTANDING OF RISK Risk may be considered from a number of different viewpoints that can be argued to form a continuum ranging from a very narrow view to a much broader understanding of the nature of risk. At the narrow or quantitative end of the scale is the view held mainly by engineers. This approach takes the stance that risk is represented by the quantitative measure of the probability
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1. Number of days needed to repair the copier. Machine Probability of Cumulative Random number repair time repair time P(y) probability range, r2 1 0.2 0.2 0.00 - 0.20 2 0.45 0.65 0.21- 0.65 3 0.25 0.9 0.66 - 0.90 4 0.1 1 0.91 - 1 2. Intervals between successive breakdowns: The probability distribution of the random variable varies between the times of 0 to 6 weeks, with the probability increasing as time goes on. This can be approximated by the function F(x) = x/18
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