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A probability function ,p(x) = Pr( X = x) or a density function ,f(x) (for which areas under the curve correspond to probabilities) Mean (or expected value ) of RV, E( X ) The typical value Standard deviation , SD( X ) A measure of the spread of the distribution The typical deviation from the mean 1 Y = a b XQuestion Prove that if, for any a, be R", f(b) – f(a) Vf(a)*(ba) then f (x) is convex for XER" This question hasn't been solved yet Ask an expert Ask an expert Ask an expert done loading Help me to prove in optimization techniques Show transcribed image text Expert AnswerJan 28,  · Example 44 Let f X → Y be a function Define a relation R in X given by R = {(a, b) f(a) = f(b)} Examine whether R is an equivalence relation or not Equivalence relation are Relations which are reflexive, transitive and symmetric R = {(a, b) f(a) = f(b)} Check reflexive Since f (a)

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22 3 Continuous Functions If c ∈ A is an accumulation point of A, then continuity of f at c is equivalent to the condition that lim x!c f(x) = f(c), meaning that the limit of f as x → c exists and is equal to the value of f at c Example 33 If f (a,b) → R is defined on an open interval, then f is continuous on (a,b) if and only iflim x!c f(x) = f(c) for every a < c < bDec 10, 08 · (xbc)/a (xab)/c (xca)/b =3 LCD abc Multiply each term of the equation by the LCD bc(xbc) ab(xab) ac(xca) = 3abc bcx b^2c bc^2 abx a^2b ab^2 acx ac^2 a^2c = 3abc2 (a) Define uniform continuity on R for a function f R → R (b) Suppose that f,g R → R are uniformly continuous on R (i) Prove that f g is uniformly continuous on R (ii) Give an example to show that fg need not be uniformly continuous on R Solution • (a) A function f R → R is uniformly continuous if for every ϵ > 0 there exists δ > 0 such that f(x)−f(y) < ϵ for all x

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After cracking the 'sum of cubes' puzzle for 42, researchers discover a new solution for 3Question (2) We Say A Function F (a,b) R Is Strictly Increasing If F(x) < F(y) For Any A < X 0 For Any Z E (a,b), Then F Is Strictly Increasing (Hint Mean Value Theorem) This question hasn't been answered yet Ask an expert Show transcribed image text Expert AnswerThe formula for change provides a model to assess the relative strengths affecting the likely success of organisational change programs The formula was created by David Gleicher while he was working at Arthur D Little in the early 1960s, and refined by Kathie Dannemiller in the 1980s

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Intuitively, a function is a process that associates each element of a set X, to a single element of a set Y Formally, a function f from a set X to a set Y is defined by a set G of ordered pairs (x, y) such that x ∈ X, y ∈ Y, and every element of X is the first component of exactly one ordered pair in G In other words, for every x in X, there is exactly one element y such that theX b g ^ ̎ ȓ ʏ ̃ ^ ̎ _ ʏ ̃ ^ ͎g p ɂ ăp b h Ƃ̊Ԃ ٕ ̕t C R W ̈Ⴂ ɂ Č Ԃ o A ^ ̕\ ʂɍׂ ؁i R h ̋؁j ł Ă ܂ ܂ B R Ԃ̓ ^ ƃp b h ̐ڐG ʐς ቺ ̂ŁA ̕ C R u L \ ቺ Ă ܂ Ƃ͔ ܂ BA is the set of all books in a library of a college R = {(x,y) x and y have same number of pages} Since (x, x) ∈ R as x and x have the same number of pages ∀ x ∈ A

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Problem 8 (1) Suppose fis a realvalued continuous function on R and f(a)f(b)Title 025pdf Author DoeringDaniel Created Date PMThe problem is roughly speaking the following If f U → R m is a differentiable function (where U ⊂ R n is open) and if x th, x, h ∈ R n, t ∈ 0, 1 is the line segment in question (lying inside U), then one can apply the above parametrization procedure to each of the component functions f i (i = 1, , m) of f (in the above

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Aug 13, 15 · CHKDSK /f /r /x when to use each or all three in a command, please explain what is happening with two computers with identical hardware and similar files Hi, Often I run CHKDSK /F /R on two laptop computers that are the same model They have very similar files and software The sizes of the hard drives and files are nearly the sameMar 23, 21 · It also includes the functionality of /f /b NTFS only It clears the list of bad clusters on the volume and rescans all allocated and free clusters for errors It includes the functionality of /r Use this parameter after imaging a volume to a new hard disk drive /vX/(bca) = y/( cab) = z/(abc) = k There are three fractions Use the following properties of fractions 1 We know that if both numerator and denominator of a fraction p/q are multiplied by the same term, it remains the same

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Aug 18, 08 · A(xB) = C(xD) Multiply it out AXBA = CX CD Isolate X to one side of the equation AX CX = CD BA Factor out the X term X(AC) = CD BA Divide by the factored term to find XFormula Sheet 1 Factoring Formulas For any real numbers a and b, (a b)2 = a2 2ab b2 Square of a Sum (a b)2 = a2 2ab b2 Square of a Di erence a2 b2 = (a b)(a b) Di erence of Squares a3 b3 = (a b)(a2 ab b2) Di erence of Cubes a3 b3 = (a b)(a2 ab b2) Sum of Cubes 2 Exponentiation Rules For any real numbers a and b, and any rational numbersConversely, assume that f(f−1) = C for all C ⊆ Y but that f is not ontoThen there exists y∈ Y such that for all x∈ X, we have y6= f(x) Let C= {y} Then f−1 = ∅ and f(f−1) = ∅ 6= C since y∈ C ContradictionHence, f is onto Thus, f is onto if and only if f(f−1) = C for all C⊆ Y 8(a) Claim f(A∪B) = f(A) ∪f(B)

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