If n=3, expand µ = a"x¡x¡

Q: Suppose we have some approximation N(h) to M, and we know that N(h) = M + C¡h+ C2h² + C3h³ +0 (h*) .…

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Q: E Fine the lowing SWAWSFSS t forattete grad meghit of a fa afal compase decompose 8orea

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Q: For what values of p is the improper integral ro* dx convergent ? Op>1 Op>1 Op<1 Op<1

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Q: Without expanding completely, find the indicated term(s) in the expansion of the expression.

A: Given, x1/2+y1/28 where n=8 total number of terms =8+1=9 middle term =n2+1 82+1=5 5th term is a…

Q: The Weber-Fechner law states that if Y is the physical intensity of sound and X is the perceived…

A: From the given information, fY(y)=ye-y22, y&gt;0 And X=klog(Y)Xk=logYeXk=Yexk*1k=dydx

Q: Let X - N(H, o?). Show that the MGF of X is etu+o²

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Q: (b) Evaluate the following antiderivative. x In xdx

A: ∫xlnx dx By integrating by part;∫xlnx dx = lnx×∫x dx - ∫dlnxdx×∫x dx dx                     =…

Q: Let n e N, s > 0, a > 1. Show that n! 1"e" dr sn+1 Inz dr 1 (a – 1)2

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Q: Calculate Bühlmann's k for aggregate losses. (A) Less than 1 (B) At least 1, but less than 2 (C) At…

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Q: 18 For which numbers a does x,+, = a{x,– x) converge to x* = (a – 1)/a?

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Q: The De Moivre-Laplace approximation fails to solve :Bernoulli trials when a) N, k is large and Np is…

A: N is number of trials  K is number of success  P is probability of success

Q: popula ty that least th st of fo

A: It is an important part of statistics. It is widely used.

Q: Find the constant term in the expansion

A: We have to solve the problem

Q: れお! /0 fi23)=4 4 (か) 2,十 F) Eanals it Ofiles)= 12 D Not if tha above

A: Given: Fx,y = x3y2 To find: Fx2,3 We know that Fxx,y is differentiation of Fx,y with respect to x ,…

Q: 19. f' "'In rdr r'In r dr

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Q: d) f(2) = In (In z)

A: As requested 4(d) to be solved 4(d) fx=lnlnx

Q: (11) When the conditional density of X given Y = y E (0, 1) is 2x fxjY=y(x) = y < x < 1. 1 – y2 '…

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Q: Find the most general antiderivative. 7 9) SWi-Zndt

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Q: (b) Define B C e? by B = {x € l² : E, nlæn[² < 1}. Show that B is compact.

A: It is defined that  B=x∈l2 : ∑n=1∞ nxn2≤1 To prove that B is compact. It is enough to prove that B…

Q: B// Evaluate the following integral: fx³ n* dx.

A: We integration by parts and logarithmic properties  eln(x)= x  ln(mn)= n ln(m)

Q: The interval [0,5] is partitioned into nn equal subintervals, and a number xi is arbitrarily chosen…

A: The given interval is [0,5]. Find the xi.

Q: Show that if $a_{n}&gt;0$ and $\Sigma a_{n}$ is convergent, then $\Sigma \ln \left(1+a_{n}\right)$…

A: Here, we are given that an &gt; 0 and series is convergent. We need to prove that: is convergent.…

Q: 3) For which a does converge? Justify your answer. n(ln n)ª n=2

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: (i) Find the constant term in the expansion of x+-

A: You have given 3 different questions in picture, without mentioning any particular questions. We can…

Q: Find the Gomplex sdutiona to the e/s 4. (You maly expres the latems in Gmiblex Polat fom).

A: We need to find the complex solutions corresponding to z4-[(1+i)/√2]=0. The solution needed to be…

Q: 20) The figure below gives the US consumption of petroleum over a 10 year period. Estimate the…

A: The given chart is  To find: the average consumption .

Q: 2. Let X~N(u, o2). Show that the MGF of X is etHtc²a².

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Q: E (n!)² (K)! Fan what e is convergent ?

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Q: The name of an expression like Ef{x;)Ax is: i=1 Infinite sum Differential sum Rectangular sum…

A: follow 2nd step

Q: Suppose that q # 1 is a constant. Calculate the sum n Sn =E kg* = q+ 2q² + 3q³ + • ..+ ng" k=1

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Q: tue velue of tme integreed 0.53 ) vitxs de with an emor less tuam 0.001. Romd Jorr Auuy Jour Ayuer…

A: The objective is to find the value of the integral ∫0.230.53 1+x3dx Use binomial expansion to obtain…

Q: Integrate the following: ,S (x4 – 5æ³ + 6) dæ - 1. So(1- r)*dz su(1– 2.

A: These questions are related to indefinite integration, we will use use integration formulas and…

Q: M N * LN = MO SS SAS AAS AONL E AONM ALON E AMON ALNO S AMON

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Q: S F(s) %3D (s+5)6

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Q: If (an) tends to infinity and (b,n) is bounded, with bn > 0 for all n, then (an/b,) tends to…

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Q: Find the rots of Z'+1= d. Hint s i - e

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Q: 1. f(x) da converges, then If f(x) ≤ g(x) for all z in [a, +∞o) and converges. g(x) dx also

A: Given

Q: Suppose the true model is given by Y = B(U)X +U where U - X and 8(U) = 1 if U >0 and =-1 if U < 0.…

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Q: See attached

A: Differentiating both sides with respect to t, we get Now, we find critical numbers of N(t)

Q: In the gas pipeline of Cactus, Tab. to Reynosa, Tamps. The cost W(Ton/hr) is determined periodically…

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Q: 6. Evaluate 1 x² + y² + x² dV, where E = { (®,g, z) |1< n? +g? +z? <4}.

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Q: If X and Y are independent and identically distributed exponential variables with parameter X = 4,…

A: We have given : X &amp; Y = independent and identically distributed exponential variables Parameter…

Q: t least one of these components will need repair within 1 year nnonont anir within 1 uear

A: Given See the handwritten solution

Q: (11) When the conditional density of X given Y = y E (0, 1) is 2x fx\Y=y (x) = 1 – y² y < x < 1.…

A: We know that  EXY=y=∫xfXY=yxdx Now, we have fXY=yx=2x1-y2, y&lt;x&lt;1…

Q: 5. If X-Beta(a, ß) show that E(X) = and Var(X) : aß (a+B)=(a+B+1) a+B

A: We have to show that X follows beta distribution then find expectation and variance of x with alpha…

Q: 1. Answer the following question when X.X...X is a random sample from N(u.o). |(a) Find the integral…

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Q: Let X1, ... , Xn be an iid Ber(0 ) with L(0) = 02는1 차 X %3D (1 – 0)n-L-1 *i Then a sufficient…

A: Introduction :-  We have to find out the sufficient estimator for parameter. From given function we…

Q: Given  n constants  ki (with i = 1,2,...., n) and n functions fi (x), deduce from Rules IV and V…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.