or Report page Share Share this 6.3 Probabilities Using Counting TechniquesThis is a featured page In a number of different situations, it is not easy to determine the outcomes of an event by counting them individually. Alternatively, counting techniques that involve permutations and combinations are helpful when calculating theoretical probabilities. This section will examine methods for determining theoretical probabilities of successive or multiple events. Permutation? or
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Homework Assignment One Solutions Probability and Probability Distributions 1. A two-sided coin is flipped twice. Calculate the probability of: a. A head on the first flip (1 point) P(H) = [pic]= 0.5 b. A tail on the second flip given that the first flip was a head (1 point) P(T | H) = P(T) = [pic]= 0.5 c. A tail on the first flip and a head on the second flip (1 point) P(TH) = P(T) ( P(H) = (0.5)(0.5) = 0.25 d. At least one head on the two
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Classical Probabilistic Models and Conditional Random Fields Roman Klinger Katrin Tomanek Algorithm Engineering Report TR07-2-013 December 2007 ISSN 1864-4503 Faculty of Computer Science Algorithm Engineering (Ls11) 44221 Dortmund / Germany http://ls11-www.cs.uni-dortmund.de/ Classical Probabilistic Models and Conditional Random Fields Roman Klinger∗ Katrin Tomanek∗ Fraunhofer Institute for Algorithms and Scientific Computing (SCAI) Schloss Birlinghoven 53754 Sankt
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Frequency Probability Cumulative Probability Random No interval Category 1 $ 22.00 0.02 0.02 0.02 2 Category 2 $ 23.00 0.35 0.35 0.37 37 Category 3 $ 24.00 0.16 0.16 0.53 53 Category 4 $ 25.00 0.44 0.44 0.97 97 Category 5 $ 28.00 0.03 0.03 1 100 Category 6 0 1 100 Total 1 The probability for each cost is shown. The total of probability is 1. We find the cumulative probability to assign
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Q1 (i) Histogram for the return on Asset A Asset A –Frequency Distribution Class Intervals-Return | | Frequency | Cumulative Frequency | Class Width | Frequency Density | Probability | Cumulative Probability | -8% | -7% | 1 | 1 | 0.01 | 100 | 0.0000 | 0.0000 | -7% | -6% | 1 | 2 | 0.01 | 100 | 0.0002 | 0.0002 | -6% | -5% | 7 | 9 | 0.01 | 700 | 0.0002 | 0.0004 | -5% | -4% | 16 | 25 | 0.01 | 1600 | 0.0014 | 0.0018 | -4% | -3% | 42 | 67 | 0.01 | 4200 | 0.0032 | 0.0050 | -3% |
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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 column and whichever column the random fit into, Excel used the corresponding repair time (days) from column C. The VLOOKUP function
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44444444 Activity Optimistic a A The project is expected to take 260 days 2 . - W hat is the probability of finishing in 270 days? Project variance is computed by summing the variances of critical activities: σ2p = 11,11111111 + 69,44444444 + 136,1111111 + 2,777777778 + 11,11111111 + 44,44444444 + 44,44444444 = 319.44444444 Project standard deviation σp = 17.873 days Probability of project completed before 270 days. Z = ( 270– 260 ) / σp = 0.559 ≈ 0.56 From table 0.5 and 0.06
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the normal distribution, Z value corresponding to probability of 0.3548= - 0.3722 Optimal no of additional firefighters based on given distribution: Q*= μ+Ζσ μ=20 σ=5 Ζ=0.3772 Thus, Q*=20-0.3772(5) =18.14 Using minimum cost criteria, 18 firefighters should be added in each unit in order to cover daily absences. 3. On a given day, what is the probability that Kelley-day firefighters will be called in to work overtime? Optimal probability that demand will exceed Q*: P (Demand>Q*) =1-((Cu/
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sales would be expired. In order to anticipate the loss of sales, it is recommended to update the product portfolio by investing in the development of patented new products. LAB proposed 17 years exclusivity on Davanrik, a substance which has probability to be efficacious for depression or weight loss or both indications. Up to now LAB has completed preclinical testing and entering clinical testing. The clinical testing will take about 7 years which is divided into 3 phases. Based on the analysis
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Chapter 6 Statistical Process Control 6.0 Introduction One of the axioms or truisms in law of nature is “No two items of any category at any instant in the universe are the same”. Manufacturing process is no exception to it. It means that variability is part of life and is an inherent property of any process. Measuring, monitoring and managing are rather engineers’ primary job in the global competition. A typical manufacturing scenario can be viewed as shown in the Figure 6.1. That is if
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