5. Let f.(x) = a". Show that "0 uniformly on (0, . handwriting

Q: Show the uniformly converge to F Fn CX) = X 12 Fn (X)= X 1X€ (-10] XER %3D

A: We know that if a sequence of function has bounded derivative the uniformly convergent

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A: Given that X be a metric space . Let xn be the sequence in a metric space X. Suppose that xn has a…

Q: e z score such that pz is less th

A: we are given that the probability value is 0.7880

Q: Let X,, X2,.. . be independent, identically distributed RVs with PDF a r>1, S(x) = { xa+1 0. x 0.…

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Q: Let x be a ndom viable with pdf : f(x) k-x*. -1< x 1 find Yalue of k. [upto one decimal place]

A: Given that X be a random variable with pdf, f(x)=Kx4, -1&lt;X&lt;1 The value of K is obtained by…

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A: Given: Average value of f(x) on the interval [-4, 7] is 4.25 The formula for average value of f(x)…

Q: Find the area under the curve y = over the interval [1, 3 -

A: Given y=3xwe can use integration to find area under the curveArea=∫133xdx

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A: From the theorem stated in step two, we can see that the function is uniformly continuous and we can…

Q: 02: Suppose that X be a continuous r.v with p.d.f f(x) = 2,0<X<1,zero otherwise. Find the…

A: Solution

Q: a random varrable Y has a cumdative df fy if 04 >4 probability hat Y falls between 2land 3 find thd

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Q: ) THE PROBABILITY DENS ITY OF THE CONTINUOUS 1RANDON VAeMBLE GNEN BY for 2<x<7, f(x) = } 5…

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Q: 6. Let (x,) be properly divergent and let (y,) be such that lim(x,y,) belongs to R. Show that (y,)…

A: To show that (yn) converges to 0, given (xn) is properly divergent and (yn) is such that lim(xnyn)…

Q: Find the average value of f(x) on the interval [2, 9]given that x < 5 if 5 < x 5 if f(x) = 1 x

A: Given,

Q: Let {fn(x)} : „x ER and > 0. 1+ nx Show that ift>0, the sequence {fn(x)} converges uniformly on

A: Given: To explain the given statement as follows, To show that if t&gt;0, the sequence fnx converges…

Q: 5. Let fn(x) ". Show that z"0 uniformly on (0, ).

A: We have to use squeeze theorem here.

Q: 20. Use Simpsons' rule to numerically integrate for the n = 6, case f(x) = x on the unit interval,…

A: Using Simpson's rule to find integration Unit interval means [0,1]

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A: Given information: σ=0.25 a)  P-value for the average "fill" where no more than 0.5% of the releases…

Q: Show that f„(x) = x" (1– x") converges pointwise V x € (-1,1]. Is f„(x) converges uniformly?

A: When a sequence includes a variable, it becomes a sequence of function. A sequence of function can…

Q: • Let X be a continuous r.v; with pdf f(x) : 0 < x < 1, x, f(x) = {2 – x, 1< x < 2, 0, elsewhere.…

A: We have given that, Let X be a continuous random variable with pdf: f(X) = {  x,   0&lt;x&lt;1…

Q: 2. Find the average value of the function x2 In(x) for 1 5x<3 Show your work in evaluating any…

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Q: Prove that sina de converges but not absolutely for 0 < p < 1. XP

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Q: suppose that u=xe+ysinz and that X,y,Z Hiwt can be measured with maximum possible errorsof 180…

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Q: 3. Determine the largest interval where j(x) = Vr² – 1 is continuous.

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Q: (c) Show that fn (x) : x2+n? converges uniformly on [0, 0).

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Q: 1 Find the area bounded by the curve y=- =-=-—-—-x³-3³² x ² + 16 4 -x2 + 3x and the line y=x.

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Q: Two sequences of functions fn and gn that converge uniformly but fn In does not converge uniformly.

A: See the attachment

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A: Given: fn: A→ℝ is uniformly continuous on A ∀n∈ℕ To prove: fn→f converges uniformly on A  fn→f…

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Q: If f(x) is continuous on [-2, 3] and the average value of the function f(x) on [-2, 3] is 6. What is…

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Q: 7 Find the area under the curve y = x over the interval [1, 5]

A: Please refer to the image below

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Q: 1 Test the convergence of fsin x dx.

A: To check convergence of given integral use comparison test of integrals. Comparison test: For two…

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Q: we the kn tegrel test to det evmine sevies are Converges or discor din () Yこ0 |Y+3 eオ

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A: Test for uniform convergence of sequences: Let fn be a sequence of functions such that it converges…

Q: 1. Find the area under the curve of y on the interval [1, 4).

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Q: Suppose X has the B(20, 0.5) distrubution. Using normal approximation for X with the continuity…

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Q: 4. For U, iid uniform on [-0,0] show that – min, {U} is sufficient for 0 > 0.

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Q: Let                          fn(x) = nx/1 + nx2  (d) Is the convergence uniform on (1,∞)?

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Q: 2. By using Simpson's rule with N = 4 , 8 , and 16 Integrate the following functions

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Q: Let Z = 3W +10 where W is uniformly distributed on the interval [0,5]. Var[Z] = ?

A: Given  : Z= 3 W +10  Where W is uniformly distributed on the interval [0,5].

Q: If |fn(x)| < an for all x and Ln=1 an converges, prove tha En-1 fn(x) converges uniformly. n=1

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Q: Compute the area under the curve of f(x)= e4 1 from x = 2 to x = 5

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Q: The function f(x) = 5 divided by 4x^2 models a continuous probability for 1 ≤ x ≤ 5. How do I…

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Q: Find the area under the curve  over the stated interval. fx=x^-2/3;[1,27]

A: Area under the curve f(x) between the interval [a,b] is given by:

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!