A. Proof that the following Gamma function is: [(n+1)= n[(n)

Q: Find the Gini index for the given Lorenz curve. (Round your answer to three decimal places.) L(x) =…

A: Gini index for the Lorenz curve can be calculated as follows: Gini…

Q: 3. Are the products of the following functions even, odd or neither? a) f(x) = x³, g(x) = |x| b)…

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Q: Exponentials with different bases Show that ƒ(x) = ax growsfaster than g(x) = bx as x→ ∞ if 1 < b…

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Q: Show that the Gamma function I (s) is logarithmically convex as well as convex. Show moreover that…

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Q: 3.264 4.102 0.239 | 0.13 1.975 | 1.271 | 0.82 0.42 1.145| 0.61 | 2.408 2.12 4.11 0.87 1.942 0.32…

A: Under null hypothesis H0 : the distributions between two patients follow exponential distribution…

Q: Find the value of y at x= 1-05 from the table given below: : 1.0 1-1 1-2 1-3 1-4 1-5 0-841 0-891…

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: Kronecker delta function is 6mn = 0 ifm=n صواب Íhi

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: The gamma function, just as many of the higher-level functions, has a variety of representations.…

A: We have to explain all the marked steps.

Q: Let E[X] = 1. Evaluate 2. Evaluate [(a+k)f(a+b) r(a+b+k)r(a), a, b constants. E[X²] for k = 1. E[X]…

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Q: (b) A series of function is given in Table Q2 as: Table Q2 f(x) (389 + e') / log x (753 + e') / log…

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Q: e* – 1 Differentiate e* + 1

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Q: The current, yearly per capita growth rate (r) of a country is 0.02. The current population of the…

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Q: 43. The gamma function is defined by T(@) e-'pa-1 dt, (a > 0). (a) Prove that F'(1) = 1. (b) Prove…

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Q: 2- this beta function B(3,6) equal to : a) 1/168 b) 1/186 c) 5.95 d) none of the above

A: We have to solve the beta function

Q: (b) A series of function is given in Table Q2 as: Table Q2 f(x) (389 + eb) / log x (753 + eb) / log…

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Q: Question # x² in tems of Evaluate ( Beta) B function

A: The given integral is: ∫01x21-x512dx

Q: Q.3 (a) Derive the beta function fromgamma function and generalized the relation B(p, q) = ")r(q)…

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Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: (1) Given functions are  f(x) = (2x2-1)(x2+3)x2+1  and g(x) = (x2+8)7(2-3x2)5

Q: Find a formula of the form  f(x) = Abx  using the given information. f(0) = 5.7; the value of f…

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Q: Find a formula of the form f(x) = Ab* using the given information. f(x) = f(0) = 3.8; the value of f…

A: Given f0=3.8 and the value of f triples for every half-unit increase in x.   To Find: A formula of…

Q: . Find the exact values of the six circeular functions of e.

A: Six circular functions of 'θ' sinθ,cosθ,tanθ,cscθ,secθ and cotθ According to the question, First…

Q: The Gini index, given by 2∫10(x−f(x))dx2∫01(x−f(x))dx, is a measure of a country's income equality…

A: 2∫01(x-f(x))dx    , f(x) = x5.3

Q: Find, to three decimal places, the value of x such that e−x = x.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: The following are a few simple properties of the gamma function (a) I (n) = (n – 1)(n – 2) …·…

A: a. Γ(n)=(n-1)Γ(n-1) Γ(n)=(n-1)(n-2)Γ(n-2)Γ(n)=(n-1)(n-2)(n-3).......(1)Γ(1)Hence proved. b.…

Q: The population of a Midwestern city starts with 50, 000 people in January 2017 and grows by 20% over…

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Q: Exer. 29-30: Find an exponential function of the form f(x) = ba* that has the given y-intercept and…

A: Given: Find function of the form f(x)=bax 1) the y-intercept is 8, P(3, 1) 2) the y-intercept is 6,…

Q: Find the value or values of c that satisfy the equationƒ(b) - ƒ(a)/b - a = ƒ'(c)in the conclusion of…

A: We have fx=lnx-1 ,   2,4 Since, fx is differentiable on 2,4 and continuous on 2,4. Thus, both…

Q: Q1. [Normal to Lognormal Transformation] Show that if a random variable X ~ Normal(µ, o), then…

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Q: The population is growing more slowly. Here ƒ is the population. Then O f'(x) 0 O f'(x) > 0, ƒ''(x)…

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Q: 1. 1. The value of E(XY) is

A: Given that μ1=5.4, σ1=1.5, μ2=5.10, σ2=2, ρ=0.70 Y=6

Q: 1.9.21. Let X be a random variable of the continuous type with pdf f(x), which is positive provided…

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Q: Let X - x? (s). Find (a) E (1+2X + X²) where E (g (x)) = 6° g (x) fx (x) dx. (b) the characteristic…

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Q: 2. Given the graph below of f (x) = e* determine the limit of the following exponential functions.…

A: We have the given graph of  f(x)=ex    We have to determine the limits of the given exponential…

Q: 4.1.31 Find the exponential function of the form f(x) = c•a* that contains the two points shown…

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Q: (12) The growth of function g(n)= 2+ log(n + 15) + n-2 AN n 0o is n+1

A: Given: g(n)=2+log(n77+15)+n6-2n3+1 Now we have to find limn→∞ g(n)

Q: 0: PC (q)

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Q: The logistic function given by f(x)=1/(1+e^-x) is a bijection, whose domain is R and range is (0,1).…

A: Given: f:R→0,1, such thatfx=11+e−x f(x)  is bijective function, that means inverse of f(x) exist…

Q: 1)Begin with the formula of the Durbin Watson DW statistic and the coefficient of first order…

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Q: Find and show how to find the value of the gamma function for α = 5.5. (6.5) = 287.8853. (5.5)=

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Q: (1) Sketch a picture that explains how the following regions are transformed under the exponential…

A: Given function is  fz=ez=ex+iyfx+iy=exeiyfx+iy=excosy+isiny It denotes a circle with radius ex if…

Q: (15) A powerful detector measures the frequency of radiation over virtually the entire…

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Q: (b) A series of function is given in Table Q2 as: Table Q2 f(x) (389 + eb) / log x (753 + eb) / log…

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Q: Calculate karl Pearson's coefficient of skewness from the following data: Profits (Dollars) 70-80…

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Q: 9. Find the exponential functions of the form f(x) = ab* that pass through 1 1) (-2, 32) and (1,-) 2…

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Q: The population of a colony of mosquitoes obeys the law of uninhibited growth.(a) If N is the…

A: Since The population of a colony of mosquitoes obeys the law of uninhibited growth.  (a) If N is the…

Q: Is there any value of x that satisfies the equation below? In(x) = -e"

A: For x =0.27....equation is satisfying....I have proof it using graph...for detail go through the…

Q: 5- this beta function B(2,7) equal to : a) 1/56 b) 1/65 c) 5.95 d) none of the above

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Q: Find a function of the form y = Asin(kæ) +C or y = A cos(kr) + C whose graph matches the function…

A: Definition used -             Trigonometric function -                         y = Asin(kx)+C or y…

Q: 1- Estimate f(1.72) from the giving data using; a- Newton's forward formula. b- Newton's backward…

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.