- 6. Show that if E|X₁|' < ∞, j ≥ 2, then E|X₁ − µ|¹ ≤ 2¹ E|X₁|³. Hint: By the iterated expectation theorem - E|X₁ − µ|¹ = E{|X₁ − µ|³ ||X₁| ≥ |µ|}P(|X₁| ≥ |µ|) +E{|X₁ − µ|³ ||X₁| < |µ|}P(|X₁| < |µ|).

Q: 1. Show that limp→∞ ||||p = ||x||∞ for all x € R¹.

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Q: 7 3 Suppose that f and g are continuous and that f(x)dx = - 3 and g(x)dx = 9. Find (g(x) - f(x)] dx.…

A: Given: ∫37f(x)dx=-3 ; ∫37g(x)dx=9To find the value of ∫37 g(x)-f(x) dx=?

Q: 2. Let 1 g(x) - 1+e * (a). of the fixed point theorem are satisfied. (b). Show that g(x) has a…

A: As per bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: 4. Find the f(x) = = value of the constant b for which f is continuous at x = -1 and determine…

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Q: 3. Show that is discontinuous at x = 0 using € - 6. f(x) = (1+x³, x≥0₂ 0, 1-x², x < 0

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Q: 2. Suppose that f(x) = e * for 0< x. a. Determine x such that P(x < X) = 0.40 b. Determine x such…

A: Given:

Q: (x-2)(x+1) 5. The domain of the function x → is: (x+1)(x-2) {x]xe R,x + 0}. d. {x]x €R}. b.…

A: The given function is  f(x) = [(x-2)(x+1)]/[(x +1)(x-2)]

Q: x • e e- for x <x < ∞ f(x) elsewhere

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Q: Recall that fn-f in measure if for any e > 0, {\fn(x) = f(x) ≥ €} → 0. - Suppose |fn| ≤ge L¹. Prove…

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Q: 8. For x < 1, Σx² = 1/(1-x). (a) Find Σnx” for |x| < 1.

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Q: 5. Determine the minimum value of f(x) = e* – 3x on the interval [-1,1] [T:3] %3D

A: Topic:- Maxima minima Minimum value of f(x) is 1.

Q: (2) Let m(E) 1}) = 0. (ii) Show that lim, S f" = m({x € E : f(x) = 1}). E

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Q: 5. Suppose that f: D→D is a continuous function, and that {an} is a solution to xn+1 = f(xn), n € N.…

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Q: 4. If K = { x € N| |x- 3| 0}. Then, TC R. 6. Let V = { x € Z| x* – 9x² + 20 = 0 }. Then, IP (V)| =…

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Q: Let X ~ N(0, 1). For any € > 0, show that P(|X| > c) ≤ ²c - ??

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

Q: 4. Assume Z=X²+1 where the CDF of X, Fx(x), is defined as [0, (a) Find Fz(z). Fx(x) = {x², x < 0…

A: Given that, Z = X2 + 1

Q: * Recall that the error due to linear interpolation of the function f(x) on [xo, x1] is f"(Em) e1(2)…

A: We are given the error estimate of due to linear interpolation of the function f(x) And we have to…

Q: 45. Let f(x) = e¯* and T3(x) = 1- x + Use the error bound to show that for all x > 0, x4 If (x) –…

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Q: 12. Find the value of k that will ensure that the following function is continuous at x = 3: x² + k…

A: As we know that the function is continuous at x=a if:   limx→a-f(x)=limx→a+f(x)=finite…

Q: If f has a continuous second derivative on [a, b], then the error E in approximating IEI ≤ (b-a)³…

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Q: Determine the value of k so thatf(x)is continuous at x = 2. 2 k² - x², x < 2 f(x): = 1.5kx, x ≥ 2

A: here we have to find the value of "k".

Q: 1. Find the monotone interval of y= (x-3)2/4(x-1)

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Suppose that f (x) = e¯* for 0 < x. Determine the following: а. Р(1 < х) b. P(X = 3) С. Р(3 < X) %3D

A: The probability density function of random variable X is given by f(x) = e-x for 0 &lt; x Note :…

Q: 10. Suppose f and g are continuous functions and [ f(x)dx=7, [f(x)dx=2, and [g(x)dx =12, determine…

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Q: 4. The pdf of X is ƒ (x)=,1<x<∞. a) Calculate the value of c so that f(x) is a pdf. b) Show that…

A: Using mathematical integration

Q: 2. Let g: RR be a measurable function such that fx|g|dm <∞ (here m is the Lebesgue measure). Show…

A: The solution is given below:

Q: 3.13. Let V D(0. 1). Suppose that f e C(V) NH(V), f(0) = 0 and |f(2)| < 1 for all z e V. Show that…

A: Given V=D(0,1) which is open disk with radius less than one. which is z&lt;1 Since f∈C(V¯)∩H(V)…

Q: a. b. C. Derive the marginal pdf of X₁. Derive the conditional pdf of X2X₁ X1 and calculate E[X₂X1…

A: As per bartleby guidelines we can solve only first three subparts and rest can be reposted

Q: 6. Suppose that f(r) when > 0. Find df (r)/dr.

A: The given function is: f(x)=xex2

Q: i) If f:(x) = 0(g(x)) for each 1 <i <k then fi(x) = 0(g(x)). %3D i=1

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Q: The graph of y= Ax) is shown. e (5,-3) f'(x) 5 D -2 8

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Q: #3) For any x € R", show that ||x|| = inf{r: xerB}, where B:= {|ly|| ||y|| ≤ 1}.

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Q: Suppose S = {1, 2, 3} T = { 1, 3, 5, 7} 28. S = {x|x & S and x & T} = 29. S = {x|x€ S or x ε T} =…

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Q: Let f(x) = 3x +1 and e > 0. What is the largest d such that |x – 2| < 8 implies that |f(x) – 7| < e?…

A: Given: f(x) = 3x + 1  |x-2| &lt; ¶

Q: 3. Consider the ceiling function, g(x)=[xwhich assigns to every x the smallest integer greater than…

A: we are given a function g(x) for which we need to find domain, codomain, range, g(A) and g(A-1)