[0, 4). 4. Prove that f(x) = x² is both uniformly continuous and continuous on

Q: Let f € L'(0,1). Assume that f(t)t2"dt = 0 for all n f = 0 a.e. 1,2,3,.... Prove that %3D

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Q: • Let X1,...,Xn iid Poisson (0) such that E(X1) = 0. Suppose that Find the level a = 0.05 LRT for…

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Q: (a) Show that y for the given z = e" In x+ xy

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Q: Let ww. f(x) = x² + Mx a) Approximate to f' with step size h = 0.1 by using central difference…

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Q: Let P(z) = | tin(t) dt. Use part 1 of the fundamental theorem of calculus to determine if P(z) is…

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Q: Given that J h(t)dt = 8, for an even, continuous function h. Which of the following MUST be true?…

A: Please refer tge attached image for complete solution.

Q: Let fn E D[0, 1]. Suppose that fh g on [0, 1], and lim fn(1/2) exists. For each x E [0, 1], show…

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Q: If the WSS process {X(t)} is given by X(t) = 10 cos (100t + 0), where 0 is uniformly distributed…

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Q: A large but sparsely populated county has two small hospitals, one at the south end of the county…

A: "Since you have posted a question with multiple subparts, we will solve first 3 sub-parts for you.…

Q: 2. Let X be continous with pdf f(x) = 1/x² if 1 < x < ∞, and 0 otherwise. (a) Does E(X) exist? (b)…

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Q: *18. (section 3.4 ex 3.) Prove that if f(r) is continuous and f(z) = S() dt, then f(x) is…

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Q: (e) If f(x) is reducible over Q then f(x +a) : a E Z is reducible over Q.

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Q: (a) Let X have the following pdf : S2(x - 1) 1<z<2 S(2) = elsewhere. Compute E(X'), E(2X-1)

A: As per our guidelines we are suppose to answer first question.

Q: 1. Show (in terms of e – 8) that a function f : R³ → R defined by f (x, y, z) = (2x + 3y + 4z) is…

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Q: 4.78 Compute P(u – 20 < X < µ + 20), where X has the density function f (x) = { 6x(1 – x), 0<x< 1,…

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Q: 1. Show (in terms of e – 6) that a function f : [2, 7] → R be defined by f(x) = Vx² + 1 is uniformly…

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Q: 4. Choose and work either a) or b), NOT BOTH. (a) Show that the function f (x) = sin z for x €R is…

A: In the question given that we have to solve any one of them. Let us solve the first one.

Q: Question 8 Show using e, 8 methods that the functions f (x) = 1 and g (x) = sin r %3D 1+ x2 are…

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Q: Find the Wronskian for the set of functions {e¬*, xe¯×, (x + 1)e-*}.

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Q: Let X be a geometric with success parameter p and pdf P(X = x) = (1 –- p)*-'p x= 1,2, 3, ... 0<p< 1…

A: Consider the given pdf, PX=x=1-px-1p Consider that the mean of a geometric probability distribution…

Q: 2. Suppose the PDF of X is given by fx(x) = 5e-5x(o)(x). Find its CDF.

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Q: please answer thank you!

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Q: If 0 < f(x) < g(x) for all x and I f(x)dx diverges, then | g(x)dx diverges. 13 Select one: True…

A: Given the statement

Q: 1+ By using the definition In(1+x) = / 1 -dt, show that for a certain range of values of r, t…

A: Solution:

Q: 1 Let f (x) = ; 1 , then f (x) satisfies the - - 2 conclusion of Rolle's Theorem on 0, 1| 6.

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Q: 1. Show (in terms of e- 6) that a function f : R + R defined by f(1. y. 2) = (2x + 3y + 42) is…

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Q: prove that F(r) = 4z-3z is chaotic on the interval [-1,1]. (Hint: consider g(6) = 30 on S'.)

A: The given function: F(x)=4x3-3x The given interval is [-1,1] To prove that F(x) is chaotic: Chaotic…

Q: Find the value(s) of k that makes the function continuous over the given interval. a < k k < a S 3x…

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Q: Suppose that T(X) is sufficient for 0 and that ^e(X) is an MLE of 0. Show that ^0 depends on X…

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Q: 8. Given for C[0,1] the inner-product function (f,g)=[f(x)g(x)dx , find ||f|| if f(x) = x+1.

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Q: Find for x = x(t) defined implicitly by 25+25 x In(t) = e25xt Also evaluate dt at (t, x) = (1,1).

A: Given,25 + 25xlnt = e25xtTaking 'log' with base 'e' on both side, we getln25 + 25xlnt = lne25xtln25…

Q: If Σ An diverges then > can diverges O only if c>0 O only if c< 0 O only if c+0 O for any real value…

A: Given, the series ∑an diverges, then we have to find the values of c for which the series ∑can…

Q: Question 9 Show that (a) f (x) = ,x E (0, ∞) and (b) h (r) = e" ,x € R, uniformly continuous on R.…

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Q: 1. Suppose a increases on [a, b], a<xo Sb, a is continuous at xo, f(xo) 1, and S(x) 0 if x xo. Prove…

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Q: 1. Show (in terms of e – 8) that a function f : R³ → R defined by f (x, y, z) = (2x + 3y + 4z) is…

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Q: 11. Show that the Beta function, defined by B(x,y) = (1-t"-1 dt , for x> 0, y > 0, satisfies the…

A: the given function is βx,y=∫01tx-11-ty-1dt for x&gt;0,y&gt;0 substitute t=1-s therefore, dt=-ds when…

Q: a. The function f: RR given by f(x)=x² is twice continuously differentiable in R", and its Hessian…

A: Note: Hi! Thank you for your question. As per the guideline we can solve one question at a time in…

Q: 3) Find a value of c for which f(x) is a pdf on the indicated interval. Q11 f(x) =, [0, 1] 1+x2

A: We know that the total probability is always 1. Using that we get:

Q: et flk) = - ** = **(- at k+1 dt k+1 1 Let f(k) %3D 1 Prove that f(k) satisfies 0<f(k)s÷ k2

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Q: and that there is a deleted neighborhood U of 0 su and n 2 0. Define f(x) = x -4g(x)(1 – cos x) for…

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Q: (a) What is F(2) =-| ()dt on (0, 2|? (b) Is F(z) contimuous? (e) Is F'(z) = f(r)? Good Luck

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Q: (11) Let G(x) = 1 In(1+t²)dt. (a) Find G(1).

A: Solution Given G(x)=∫1xπ ln(1+t2)dt.We need to find the G(1)

Q: Let Xi- N co,1) and n=2 auel T= Xi+ Xz Show that Tis a %3D Sufficiency Stabisuic Statistic.

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Q: For f(x) = √ √2-4 4- ™ Of is not continuous at x = 4 Of is continuous at a Of is continuous at a 5…

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Q: Determine, with motivation, whether the following function satisfies Dirichlet's conditions on the…

A: Given: fx=cscx with fx=fx+π on -π2,π2 To check if the given function satisfies Dirichlet's…

Q: Which of the following functions has a maximum y value of 4 Oy= 4cos x y= cos 4x Oy= cos x + 4 Oy=…

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Q: Prove that by Gamma Function pit +e e-st dt %3D s2 +1

A: Gamma Function: The gamma function, denoted by is denoted by which is convergent for Some…

Q: 1. Use the Gauss forward formula with xo = 2.0,h = 0.15, n = 7 to find an estimate for f(2.5) if %3D…

A: Given: fx=xlnx. x0=2.0, h=0.15, n=7.   We can solve this by using Gauss forward formula

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.