eX(t) , (1) where X(t) = σB(t) + µt is BM with drift and S(0) = S0 > 0 is the intial value. Taking logarithms yields back the BM; X(t) = ln(S(t)/S0 ) = ln(S(t))−ln(S0 ). ln(S(t)) = ln(S0 )+X(t) is normal with mean µt + ln(S0 ), and variance σ 2 t; thus, for each t, S(t) has a lognormal distribution. 2 As we will see in Section 1.4: letting r = µ + σ , 2 E(S(t)) = ert S0 the expected price grows like a fixed-income security with continuously compounded interest rate r. In practice, r >> r, the real
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demonstrates the result in BER as a function of SNR. The relationship between BER and SNR are established for M-PSK system for three channel properties; AWGN, fast, and slow fading. AWGN channel was modeled by normal distribution. Rayleigh distribution were used for fast fading and lognormal distribution for slow fading is used to model. Three primary relationships created after the modeling are * BER to SNR relationship for BPSK, QPSK, 8-PSK, and 16-PSK for AWGN only channel * BER to SNR relationship
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................................................................................... 8 5. Discrete Probability Distributions............................................................................................. 11 6. Continuous Probability Distributions ....................................................................................... 13 7. Sampling and Sampling Distributions ...................................................................................... 15 8. Interval Estimation
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Chapter 3: Introduction to Reliability Theory Claver Diallo OUTLINE 1. Part 1: Basic Reliability Models 1. 2. 3. 1. 2. 3. 4. 5. System Reliability function Probability distributions Reliability Block Diagram Serial and Parallel Structures Stand-by Structure k-out-of n Structure Complex structure 2. Part 2: Reliability of Structures 3. Part 3: Reliability Allocation 4. References 2 2 2 2 2 2 2 2 Chapter 3 - Part 1: Basic Reliability Models SYSTEM System: a collection of components
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variable with mean 120 and standard deviation 16. Let X represent the number of components checked by an inspector in a shift. Then the total number checked is 5X, which has mean 600 and standard deviation 80. What is wrong with this argument? Assuming that inspectors' performances are independent of one another, find the mean and standard deviation of the total number of components checked in a shift. The calculation for the mean is OK, but the calculation of the standard deviation is not. Remember
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organizing, analyzing and interpreting data to make decisions. The two types of data used in the project are sampling and proportions. The methods used can be used by any professional or in any occupation. It can be used to determine the standard deviation, mean of any data among others. Part 1 In part one, each student was asked to take a tally of the 3 bags of candies bought from three different stores. And then we were asked to count the totals of each color in all 3 bags
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Due on 4/29 * Test corrections * Final Paper – Hard Copy * Final Exam – 15 questions – each worth similar points * Review midterms 1, and 2 in its entirety * Chapter 14 and 15 new material – complete the problem set on blackboard * Blue book and tables and calculator * 2 sides of 8 x10 * 14 and 15 all sections – not going to give us 30 observations and ask us to calculate the coefficient. No calculation formulas in the chapters. Put on the cheat sheet what a generic
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estimate the expected activity times. Expected time is given by (o + 4m + p) / 6 and variance is given by ((p - o)/6)2 . The reason for dividing by 6 is due to the fact that the area under the normal curve between -3 and 3 accounts for more than 99% of the total probability of 100%. In case of standard normal curve, = 1; hence -3 = -3(1) = -3 and 3() = 3(1) = 3 and the difference between 3 and -3 is 6. An example will illustrate the PERT/CPM technique. Example: The optimistic, most probable
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can be compared with the scores of others who have previously completed a test (based on a standardised sample). The scores of the candidates who previously undertook the test can be plotted in a graph that will resemble a “normal” curve. (DISCUSS PECENTILES AND STANDARDS SCORES ETC). The various forms of averages and how they are calculated Mean The mean is calculated by adding up all the numbers in a dataset and then dividing that by the number of values in that dataset. An example is given
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IT 608 Homework Complete each of the following problems using Excel. Set-up each problem as a separate worksheet in one Excel file. Clearly indicate your answer. Submit your homework (one Excel file) electronically through the Assignments on Blackboard before 9AM on final due date. Late assignments may be penalized or not accepted. Assignments posted EARLY(well before final due date) will be graded and you will have an opportunity to make corrections and resubmit for full credit. 1. Jimmy
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