(17) Define S(n) as follows: n S(n) : i(i!) = (n+ 1)! – 1 i=1 Prove Vn e N1, S(n).

Q: (a) Suppose X U (0,n), where n is a positive integer X-[X] U (0, 1). (b) Use the result of (a) to…

A: De Moivre's theorem gives an axiom for computing the powers of complex numbers. We first gain some…

Q: blem 2: Consider the following second order IVP y"(t) + 2y'(t) + y = 4e' with IC1: y(0) = 1.0 and…

A: Given y"(t)+2y'(t)+y=4et

Q: 59. Prove the general formula iwollo oi ons dx 1 x - In x – b + C %3D (x – a)(x – b) a – b - - where…

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Q: 1. Aşağıda verilen serilerin yakınsaklık ya da ıraksaklığını belirleyiniz (Yöntemleri açıklayınız).…

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Q: H) 9f zyzec then prove thal nl x=4=Z, (alogen) %3D

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Q: Z1 is complementary to ZM 22 is complementary to ZM Z1 = 2 Given: Prove: M R 2

A: Given: ∠1 is complimentary to ∠M. ∠2 is complimentary to ∠M. To prove: ∠1≅∠2 According to the…

Q: A random process X (t) is defined by X (t) = 2. cos (2 nt + Y), where Y is a discrete random…

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Q: In Exercises 23–30, find Tn centered at x = a for all n. 26. f (x) = e", a =-2

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Q: -2+z) ds over t e point (0, 0, 0)

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Q: 4. Work either (a) or (b), NOT BOTH (a) Let In = for n E N. Prove that nIn = 0. 0, n n%=D1

A: a. Given that    In=0,1n  for  n∈ℕ. And we have to prove that…

Q: 2xy + In(8 + z²), x 7v2 ', y = 9u + 3v, z = cos(4u). Find dwlðv when u = 5, v = 2. Suppose w = ,X =…

A: We have, w=2xy+ln(8+z2) x=7v2u,y=9u+3v,z=cos(4u). Point (u, v)=(5, 2)   As we can see that x, y and…

Q: 2(3) Calculate the following commutators: (a) [d/dx, x·d/dx] (b) [sin(x), cos(x)] (c) [x^2, Ĥ] ,…

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Q: -пя for all x € 0, 00). t fal(x) — же па for all z € [0, co). Find || fn||sup for all n. Prove that…

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Q: 1 1 Зі + 1 3і +2 Зі +3 1 1 Problem 2: Prove that Vn e Z such that n > 0,|| (3п + 3)! i=0

A: For any integer n where n is greater than or equal to 0. n! = n(n-1)(n-2)...3x2x1.

Q: Example 8.10. Evaluate Sº (ii) Simpson's 1/3 rule, (iii) Simpson's 3/8 rule, dx Jo. 1 + x² by using…

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Q: 7) Suppose w=rt+rs' and r= tan-' (2x² +3y), s=x²y' +3y and t = x²y² .Use the chain rule (from…

A: Given w=r2t+rs3r=tan−1(2x2+3y)s=x2y3+3yt=x2y2

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: K=Zp(t) ,then f(x)=x^p-t is irreducible over K[x]

A: GIVEN: K = Zp(t)

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: S Prove that L(cos 3t) (s²+9)

A: Given L(cos3t)

Q: 2 The half range cosine expansion of f(t) = t+ t , 0<t<1 is 2 2 f(t) S[2(3(– 1)")] cos (nnt)/n´n 22…

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Q: Show (in terms of e - 6) that a function f : [2,7] R be defined by f(z) = V² +1 is uniformly…

A: In this question, we need to show the given function f(x) is uniformly continuous.…

Q: 1. Aşağıda verilen serilerin yakınsaklık ya da ıraksaklığını belirleyiniz (Yöntemleri açıklayınız).…

A: As you have asked for only question number c, so I am only giving solution of that.

Q: The Wronskian 1. Show that the functions e", cos x and sin x are linearly independent. 2. Show that…

A: 1. The functions ex, cos x and sin x are linearly independent.2. The functions 1, sin2x and cos2x…

Q: /et A 3 8 カー (-45 Show That LA+B S ZA+B) 3-5 = At B

A: Transpose of a Matrix is defined as “A Matrix which is formed by turning all the rows of a given…

Q: 1. (a) Assume T > 0, and that the moment generating function Mx (t) of a random variable X is finite…

A: Hello! As you have posted 2 different questions, we are answering the first question. In case you…

Q: Let X(t) be a WSS Gaussian random process with ux(t) = : 1 and Rx(7) = 1 + 4 cos(7). Find

A: From the given information, Xt be a WSS Gaussian random process with μXt=1, RXτ=1+4cosτ. Consider,…

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: 3.1. Use the Neyman-Person lemma to find the best critical region of size 0.034 for testing Ho:0 = 1…

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Q: 3.1. Use the Neyman-Person lemma to find the best critical region of size 0.034 for testing Ho:0 = 1…

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Q: 27. Show that कक्या 1 Vn E Z*. T1\2i+1 2i+2. i=0 (2n + 2)!'

A: Consider the given expression. ∏i=0n12i+1·12i+1=12n+2! Consider the left side of the equation.…

Q: An M.V.U. is unique in the sense that if T, 1 M.V.U. estimators for y (0), then T, = T, almost

A: A sample statistics t is said to be unbiased estimator of population parameterγ(θ) if expected value…

Q: 7. a) Prove that for r > 0 * (E) + c. Vr2 – r²dx = vr² – x² + -1 sin 2 +C.

A: To prove: ∫r2-x2dx=x2r2-x2+r22sin-1xr+C

Q: 4.8. Show that Dirichlet's function 1, if x is a rational number, { otherwise f(x) = 0, is not of a…

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Q: 11 ComputePydz - zy'dy, nhere Dis descnbed by z² + y²s1. -1/2

A: Given an integral : ∫∂D x2y dx - xy2 dy  where D is : x2+y2≤1 We need to compute the integral.

Q: 10. Show that S t2 if 0 1, 2(1 - e-) then Ldf %3D

A: Laplace of differential equation.

Q: дz (B)If Z = f(x, y), x= s² - t², y = 2st. Prove that s მs 2 (s² + t²) of əx

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Q: Q3/ prove fry = fyx if f(x,y) = x + xy – 5x³ + In(x2 + 1)

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Q: 4. Exercise §3.4 #47. Let n €Z with n> 0. Prove that E - a(n)

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Q: 2 The half range cosine expansion of f(t) = t + t,0<t<1 is 00 2 2 f(t) = + n [2(3(-1)")] cos cos…

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Q: 1. Prove that L(t)=. s2

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Q: 18. (2) = t"(-t)" dt, show that F(m). m! +1, n+1 %3D m and n are positive integers.

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Q: -B/ls//E-x] in (6.14) is distributed as at =

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Q: 2) Consider the sinusoidal signal x(t) =cos(500rt + 0), and suppose that this signal is sampled,…

A: please see the next step for solution

Q: Let M, = Z, – Z;-1, Zo = 0, where {Zn, n21} is a martingale. Show that E(M,„Z„-1] = 0

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Q: B. Prove by direct proof general. P: Vn e ZE, (n – 1) (n+ 1) e Z,

A: I have solved B; you just need to expand (n-1)(n+1) and then use the fact that square is always…

Q: If f(x,y,z)=z In(x²ycosz), then fz is O 2z X OZ y O2z y O In(x²ycosz) - ztanz <|N

A: This question is related to partial differentiation, We will solve it using given information.

Q: D Reduce the Q.F 22,xz t 22,X3 2ズュズ3 weag ayf of oothogonal toans fermation by an Ans: y+92-295

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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.