MA1310 College Mathematics II Study Guide MA1310 College Mathematics II Study Guide DISCUSSION 1.1 (3.5 HOURS) Title: Solving Real-Life Problems Using Sequences Read the following old English rhyme from one of the Rhind Mathematical Papyrus texts: As I was going to St. Ives I met a man with seven wives Each wife had seven sacks Each sack had seven cats Each cat had seven kits [kittens] Discuss the following questions: 1. Assuming that the speaker and the man with seven wives met while traveling
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A short introduction to the Arena simulation software Version 1.0 dr. Kees Jan Roodbergen dr. Iris F.A. Vis © 2007 ©2007‚ K.J. Roodbergen and I.F.A. Vis All rights reserved. No part of this publication or the related models may be reproduced in any form or by any means without prior permission of the authors. 1 Contents 1 2 Introduction ................................................................................................................ 6 Terminology .................
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IB Physics Internal Assessment Andy Tang Research Question In this internal assessment‚ I am given a cantilever to find the physical properties of it. I decide to investigate the relationship between the force I act on one side of the cantilever and the maximum acceleration the tail can reach. This experiment will be also showing the elasticity of the cantilever. Since I pull down one side of it and fixed the other side‚ when I cut the string‚ it will bounce up and down until all the internal
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maintaining and repairing a car? (Ans: 374) 4. The time to failure of a component in an electronic device has an exponential distribution with a median of four hours. Calculate the probability that the component will work without failing for at least five hours. (Ans: 0.42) 5. A company has two electric generators. The time until failure for each generator follows an exponential distribution with mean 10. The company will begin using the second generator immediately after the first one fails
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multiple-channel waiting lines. Understand how the Poisson distribution is used to describe arrivals and how the exponential distribution is used to describe services times. Learn how to use formulas to identify operating characteristics of the following waiting line models: a. Single-channel model with Poisson arrivals and exponential service times b. Multiple-channel model with Poisson arrivals and exponential service times 5. Know how to incorporate economic considerations to arrive at decisions concerning
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Exponential Distribution Introduction An electrical engineer who is in charge of an electrical wiring in a premise wants to know the number of faults in a given length of wire and also the distance between such faults. He can analyzed the number of faults using the Poisson distribution. The number of faults along the wire maybe shown to give rise to the exponential distribution as defined below: Definition The general formula for the probability density function of the exponential distribution
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ST421 Exercise 1 — Solutions 1. Note that P (uj ≤ Xj ≤ vj ) = e−λuj − e−λvj ‚ and fXj (x|uj ≤ Xj ≤ vj ) = λe−λx /{e−λuj − e−λvj }. Hence‚ Xj (λ) ≡ Eλ (Xj |Xj ∈ [uj ‚ vj ]) = 1 uj exp(−λuj ) − vj exp(−λvj ) + . λ exp(−λuj ) − exp(−λvj ) The log-likelihood function based on the full sample is n ∑ l(θ) ≡ l(θ; X1 ‚ · · · ‚ Xn ) = n log λ − λ Xj ‚ j=1 which yields the MLE based on full sample θ(X1 ‚ · · · ‚ Xn ) = n/ ∑ 1≤j≤n Xj . Now the E-step is Q(λ) = Eλ0 {l(θ)
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MANAGEMENT RESEARCH PROJECT INTERIM REPORT ON Analyze Big Bazaar’s customer queues at cash counter and reducing customer waiting time by proposing the optimum number of cash counter. Submitted By: Ravi Kumar Mishra Enroll no: 07BS3347 Batch: (2007-09) ICFAI BUSINESS SCHOOL‚ LUCKNOW
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Unit 8 Exponential Functions Review Packet Short Answer Graph the exponential function. 1. 2. 3. An initial population of 505 quail increases at an annual rate of 23%. Write an exponential function to model the quail population. 4. Write an exponential function for a graph that includes (1‚ 15) and (0‚ 6). 5. For an annual rate of change of –31%‚ find the corresponding growth or decay factor. 6. Graph . 7. The half-life of a certain radioactive material is 85
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5. To find the equation of the exponential function that pass through (0‚-1)‚(-1‚-3)‚(-2‚-9) with x-axis as asymptote: Formula: y=a(bx) y-intercept (0‚-1) 1) Point 1 (-1‚-3) 2) Point 2 (-2‚-9) (-3)=ab-1 (-9)=ab-2 -3/b-1=a (-9)/b-2=a Find b- Since a=a Therefore -3/b-1= (-9)/b-2 -3(b-2)= -9(b-1) -3(b-2)-9(b-1)=0 b-1(-3b-1-9)=0 b-1=0 or (-3b-1-9)=0 1/b=0 -3b-1=9 1(0)=b b-1=3 b=0 1/b=3 1=3b b=1/3 Since the plotted curves of exponential function never go above the x-axis‚ b must
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