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2 Pages

### hw04_11_06

Course: STAT 425, Fall 2009
School: Michigan
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Word Count: 702

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Stat 425 Problems due 4/11/06 Chapter 7: 9a (there can be more than one ball in an urn), 11, 32, 34 A) An environmental engineer measures the amount (by weight) of particulate pollution in air samples of a certain volume collected over the smokestack of a coal-operated power plant. Let Y1 denote the amount of pollutant per sample collected when the cleaning device on the stack is not operating and let Y2 denote...

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Michigan - STAT - 425
Stat 425EXAM 3Name:Exam Instructions: Use a separate piece of paper to answer each question. Label the paper with the question number and your name. Try to show as much work as possible and explain your thoughts. There are 3 problems on this te
Michigan - STAT - 425
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Michigan - STAT - 425
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Michigan - STAT - 606
Sorting, Ranking, Indexing, Selecting The denitions of sorting, ranking, and indexing should be clear from the following example:inalxedRan kedOrigInde3 1 2 6 4 06 2 3 1 5 44 2 3 6 5 1 If we can index and sort, we can rank: if v is
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Likelihoods The distribution of a random variable Y with a discrete sample space (e.g. a finite sample space or the integers) can be characterized by its probability mass function (pmf):P (Y = y) = f (y). For example, suppose Y has a geometric dist
Michigan - STAT - 600
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Michigan - STAT - 547
Statistics 547 Problem Set 4 Due Tuesday, April 23 1. Get the les orf coding.fasta and NotFeature.fasta from ftp:/genome-ftp. stanford.edu/pub/yeast/ (you will nd the les in two dierent subdirectories). For each sequence in each of the two les, compu
Michigan - STAT - 547
Machine LearningIntroduction Suppose X and Y follow a joint distribution P (X, Y ). We observe X and wish to predict the corresponding value of Y . 1. If Y is numerical, the best predictor is E(Y |X). 2. If Y has a nite sample space, then the best
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Today Today: Chapter 9Assignment: 9.2, 9.4, 9.42 (Geo(p)=&quot;geometric distribution&quot;), 9-R9(a,b) Recommended Questions: 9.1, 9.8, 9.20, 9.23, 9.25Estimation Can use the sample mean and sample variance to estimate the population mean and varian
Michigan - STAT - 405
Today Today: Chapter 9Assignment: 9.2, 9.4, 9.42 (Geo(p)=&quot;geometric distribution&quot;), 9-R9(a,b) Recommended Questions: 9.1, 9.8, 9.20, 9.23, 9.25Example Suppose X=(X1, X2,.,Xn) represents random sample from a population Suppose the population
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The Julia SetIn the last lesson, we described the Julia set while studying iteration of functions in the complex plane. In this lesson, we will take a detailed look at the structure of the Julia set and elucidate some of the Julia sets salient featu
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The Mandelbrot SetThis lesson will concentrate on one of the most widely recognized icons of the field of chaos, dynamics and fractals - the Mandelbrot set. The appearance of the set will be familiar to many, and one image of it is given below. The
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FractalsIn several of the lessons we have described objects as fractals, for example, the Julia set known as the `Rabbit.' *Please insert julia_4.gif* The important property that we were trying to capture by the label `fractal' was the property of s
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Quadratic Functions. What's So Chaotic About Them?In the previous lesson on Graphical Analysis, we looked at the Julia set. This set was obtained by looking at all the points in the complex plane. Each point in the complex plane was used as a starti
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Iteration and the Complex PlaneIn the previous lessons, we studied iteration of functions that take a real number as an input and a real number as an output. The lesson on quadratic functions gave many examples of how the iteration of functions that
Michigan - MATH - 548
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Math 216050 Exam 1, 7 October 2002 Prof. Gavin LaRose page 1 of 4Name: Lab section: (8,9am,12,1pm = 51-54)For all problems, SHOW ALL OF YOUR WORK . While partial credit will be given, partial solutions that could be obtained directly from a calcu
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Math 216040 Exam 2, 20 March 2003 Prof. Gavin LaRose page 1 of 4Name: Lab time (circle): 10am 11am 2pm 3pmFor all problems, SHOW ALL OF YOUR WORK . While partial credit will be given, partial solutions that could be obtained directly from a calcu
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Math 216040 Final, 23 April 2002 Prof. Gavin LaRose page 1 of 4 problem: total pts: score: Name 2Name: Lab section: 1 24 2 14 3 10(2 points)(10,11am,2,3pm = 41-44) 4 22 5 22 6 6Please do not fill in:For all problems, SHOW ALL OF YOUR WORK .
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Math 216040 Exam 1, 11 February 2003 Prof. Gavin LaRose page 1 of 4Name: Solution Lab time (circle): 10am 11am 2pm 3pmFor all problems, SHOW ALL OF YOUR WORK . While partial credit will be given, partial solutions that could be obtained directly
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Michigan State University - CSE - 320
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( x, x) x y=x 50 - x w s@~g{y 5a~ { w { x r q i r 8 d 8 r m 8 6 h 8 w f n q 6 8 6 9 h h q 6 q 8 r P r 9 i h q 6 q r P h q g}Q3ciHy3Qx H&amp;ixP&amp;tP&amp;xPfsjP36xhDzHDFH3A e 3sjPiHrqotAqxPw5HDP3t6qro3xAe&amp;DphDotA6 q i q6wP i6 e if
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* Reading Outline, Sec4.5 *-* Vocabulary/Definitions * - Tips for Modeling Optimization Problems* Understand *1. Find a mathematical model for the surface area of a rectangular boxwith a square base that has a volume of 10 cubic meters.
* Reading Outline, Sec4.4 *-* Vocabulary/Definitions * - Fixed costs - Economy of scale - Revenue - Profit, as a function of revenue and cost - Marginal cost and marginal revenue, as average rates of change - Marginal cost and marginal rev
* Reading Outline, Sec4.1 *-* Vocabulary/Definitions * - If f'&gt;0, then f is\dots - If f'&lt;0, then f is\dots - If f'&gt;0, then f is\dots - If f'&lt;0, then f is\dots - Local minimum or maximum - Critical point (what are the two meanings?) - Firs
* Reading Outline, Sec1.5 *-* Vocabulary/Definitions * - Radian - Conversion between degrees and radians - Arclength on a circle as a function of the angle - (x,y) on a unit circle and cos(t), sin(t) - Amplitude - Period - How cos(t) tran
* Reading Outline, Sec5.3 *-* Vocabulary/Definitions * - Interpreting integrals as sums and the meaning of f(t) dt - The Fundamental Theorem of Calculus - The average value of f(x) between x=a and x=b - The geometric interpretation of the av
* Reading Outline, Sec1.7-1.8 *-* Vocabulary/Definitions * - Continuity of a function - Which functions are continuous - The Intermediate Value Theorem - Limit - Right- and left-hand limits - How a limit may not exist - What a limit at in
* Reading Outline, Sec2.3 *-* Vocabulary/Definitions * - How can we estimate, from a graph, the derivative of a function at a point? - Derivative function - Implication of f'&gt;0 and f'&lt;0 - How to estimate derivatives from tabular data (how ca
* Reading Outline, Sec1.6 *-* Vocabulary/Definitions * - Power function - What `dominate' means - Which of exponentials or power functions dominate - Polynomial function - Degree of a polynomial - Number of ``turns' of a polynomial - Zero
* Reading Outline, Sec3.3 *-* Vocabulary/Definitions * - The Product Rule - How the product rule is derived - The Quotient Rule - How the quotient rule is derived* Understand *1. Find (d/dx)(3x e^x)2. Find (d/dx)(3x/e^x)
* Reading Outline, Sec1.1-1.2 *-* Vocabulary/Definitions * - Function - The Rule of Four - The Domain of a Function - When a Function is Linear - Difference Quotient - The Equation of a Linear Function - What `y is proportional to x' mean
* Reading Outline, Sec2.5 *-* Vocabulary/Definitions * - The second derivative - What f' says about f' - What f' says about f - What it means about the rate of change of a function if f'&gt;0 (or &lt;0) - Average acceleration - Instantaneous acc
* Reading Outline, Sec3.1-\S3.2 *-* Vocabulary/Definitions * - The effect of a constant multiple of a function on its derivative - (c f(x)' = - (f(x) + g(x)' = - The power rule: (d/dx)(x^n) = - The derivation of (x^{-2})' = -2 x^{-3} fro
* Reading Outline, Sec5.1 *-* Vocabulary/Definitions * - Estimating distance traveled from data - Representing distance traveled as a sum of rectangular areas - Finding the difference between over- and under-estimates for distance travele
* Reading Outline, Sec1.3 *-* Vocabulary/Definitions * - The relationship of the graph of c f(x) to that of f(x) (c&gt;0 and c&lt;0) - The relationship of the graph of f(x-h) to that of f(x) - The relationship of the graph of y-k to that of y -
* Reading Outline, Sec2.6 *-* Vocabulary/Definitions * - Differentiability - Conditions under which a function will not be differentiable - Does continuity imply differentiability? - Does differentiability imply continuity?* Understand *
* Reading Outline, Sec6.1 *-* Vocabulary/Definitions * - Antiderivative - Family of Antiderivatives - Sketching f given f': behavior of f when f'&gt;0, f' is increasing, etc. - Using the Fundamental Theorem to find actual values of f(x) given f