following two conditions on the random vector [pic]are met: 1. [pic] 2. [pic] the best (minimum variance) linear (linear functions of the [pic]) unbiased estimator of [pic]is given by least squares estimator; that is‚ [pic]is the best linear unbiased estimator (BLUE) of [pic]. Proof: Let [pic]be any [pic]constant matrix and let [pic]; [pic] is a general linear function of [pic]‚ which we shall take as an estimator of [pic]. We must specify the elements of [pic]so that [pic]will be the best unbiased
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losing its functions. For many years‚ the family has had a set of functions that every family has had to follow in order to fit in with society. Some of these functions include social control and the gender-role socialisation. Some Sociologists that have explored these functions are Murdock and Parsons. Murdock looks at reproductive‚ sexual and economic functions. Whereas‚ Parsons looks at the primary socialisation of children and the warm bath theory. I will be looking at these functions and assessing
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Trigonometry and Statistics) A. Functions 1. Demonstrate knowledge and skill related to functions in general 1.1 Define a function 1.2 Differentiate a function from a mere relation * real life relationships * set of ordered pairs * graph of a given set of ordered pairs * vertical line test * given equation 1.3 Illustrate the meaning of the functional notation f(x) 1.4 Determine the value of f(x) given a value for x B. Linear Functions 1. Demonstrate knowledge and
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.........3 RECOMMENDED 2-UNIT OPTIONS......................................................4 MATHEMATICAL MODELLING............................................................4 UNIT 1: ALGEBRA‚ GEOMETRY AND CALCULUS MODULE 1 : BASIC ALGEBRA AND FUNCTIONS...........................7 MODULE 2 : TRIGONOMETRY AND PLANE GEOMETRY .............18 MODULE 3 : CALCULUS I ..............................................................23 UNIT 2: ANALYSIS‚ MATRICES AND COMPLEX NUMBERS MODULE 1 : CALCULUS II .
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of a and b 2) A function f is defined as f(x) = for x 1 = - for x = 1. Show that f(x) is differentiable at x = 1 and find its value 3) Let f(x) = if x 2 = k‚ if x = 2. If f(x) is continuous for all x‚ then find the value of k. 4) Let f(x) be a function of x defined as f(x) = ‚ x 1 = ‚ x = 1. Discuss the continuity of function at x = 1 5) Determine
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n calculus‚ Rolle’s theorem essentially states that a differentiable function which attains equal values at two distinct points must have a point somewhere between them where the first derivative (the slope of the tangent line to the graph of the function) is zero. ------------------------------------------------- Standard version of the theorem [edit] If a real-valued function f is continuous on a closed interval [a‚ b]‚ differentiable on the open interval (a‚ b)‚ and f(a) = f(b)‚ then there
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Structured program list. First unit: Sets. In this unit the fundamental concepts of the theory of sets is addressed to provide the tools and the language of operation for subsequent units. Second unit: numbering systems. In this unit‚ we address numbering systems of different cultures until the one’s used current day‚ highlighting the importance of ten based numbering system (decimal)‚ which will be developed in depth by tackling its properties through the next unit. Unit Three: The field
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looking for at Store A. In Store A‚ the bracelet without charms costs $85 and each charm costs $15. A. Use function notation that models the total price of the bracelet and how that price is based on the number of charms. Explain the reasoning behind your equation. 15W=85 IN ORDER TO FIND THE NUMBER OF CHARMS YOU NEED YOU HAVE TO DIVIDE. B. What would be a reasonable domain for this function based on this scenario? Explain why this is a proper domain. C. If Marco and his sisters have saved $250
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to evaluate logs‚ trigonometric functions‚ and exponents? This ability is due in large part to the Taylor series‚ which has allowed mathematicians (and calculators) to approximate functions‚such as those given above‚ with polynomials. These polynomials‚ called Taylor Polynomials‚ are easy for a calculator manipulate because the calculator uses only the four basic arithmetic operators. So how do mathematicians take a function and turn it into a polynomial function? Lets find out. First‚ lets assume
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the origin of the leisure class. Specific Areas to Be Covered Veblen examines the demand and consumption of the upper classes of society in terms that are not traditionally used in economics. In using terms such as conspicuous consumption‚ pecuniary emulation and conspicuous leisure‚ Veblen is basically doing a demand and supply analysis of the classes of society. He looks at the consumption patterns of the upper class because this affects the rest of society through the mechanism of emulation
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