Let X ∼ Geom(p), let n be a non-negative integer, and let Y ∼ Bin(n, p). Show that P(X = n) = (1/n)P(Y = 1).

Q: 5. Prove that So*(y – 0)dydr =

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Q: OLet @ = (0,1)n Q = {x€ @104 x<1}. Prove that %3D 2) 2000m

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Q: Let X N (u,1) of size n. Obtain UMVUE for M.

A: We will use Lehmann-Scheffe theorem to find the uniformly minimum variance unbiased estimator for μ.

Q: (b) En=1 m

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Q: Use Newlon's Me thod with the runclion $r(x)=x^{2}-2$ and inilial value $x_{0}=3: to calculate…

A: Givenf(x)=x2-2            and     x0 =0 newton method  xn+1=xn-f(xn)f'(xn)

Q: Using the Convolution Theorem, what is L[h(t)]?

A: In this question, we use the convolution theorem to find the Laplace transform of the given function…

Q: Q Find the deriva tive using the de fini tion (x)

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Q: Prove that cosh-z = In (z + vz? - 1) %3D

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Q: dy is If y = In then cosh z

A: Given,          y=lnxcoshx

Q: Find the limits in Exercise

A: We know that, limx→∞sinxx=0            ⋯⋯1limx→∞ax=0            ⋯⋯2      for any constant a

Q: Use Euler's method to obtain a four-decimal following: approximation for t (4 y=2Xy, yC)=1; yU5) =?…

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Q: alue of the pur C: |z| = (:-1)(z-

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Q: Evaluate the integral ſſ /ydA, where T- triangle with vertices (1,0), (0, 1), (1, 1).

A: Let us consider the double integral  I=∫ab∫f(x)g(x) f(x,y) dydx    or I=∫ab∫f(y)g(y) f(x,y) dxdy…

Q: Is it possible to find a number  n  such that is ∫0∞  xn dxconvergent?

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Q: Q3: show that: S yi va -y dy =na² where a is a positive constatnt

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Q: Q6:-Prove that: y" = 1 if y=;csc (tan"

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Q: For z C, show that the solutions of cosh(z) = 1 are z= i2km, for ke Z.

A: We need to prove that the solutions of the equation: cosh(z)=1 are z=i2kπ, where z∈ℂ, k∈ℤ.

Q: Prove that in the pairs of positive numbers ¤, y for æ² + y° = r the sum a+y is greatest when z = y.…

A: Here we solve the given problem of calculus.

Q: OVESTON Prove that A is inveitine if at0 and at b l Gind The pivos 9 A %3D a a

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Q: Evaluate the improper intergal 1 dx using the residue (x² + 16)² theorem.

A: We need to evaluate integral.

Q: (b) Compute r if: arctan r + arctan 1 = 2 ( arctan z arctan

A: tan-1x+tan-11=2tan-1x-tan-113

Q: 1) Prove that Ym,n EN such thert m¢ nt = n<m using the princdple of in duction!

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Q: Let X and Y be independent and distributed as N(u, 1). Is T = X-Y sufficient?

A: According to factorization theorem, If the likelihood function L(x,θ) can be expressed in the form…

Q: The evaluation of S V1 + tan2x dx is C In(V2) +1 In(vZ+1) C In(vZ-1) O-In(vZ+1)

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Q: cancer u alcurate 5th on diagnostic test is 9s 2 those who halse A 'cancer cnd on those wno do not

A: Given that, As the test is 95% accurate for both who have cancer and who don’t, therefore the…

Q: y = sech*x = In(_+ V1- x², sechx = In(- 1+ V1-x² Prove that .... ..

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Q: 2.Prove that I (sinwt) : s2+w?

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Q: △XYZ is given with X(2, 0), Y(0, −2), and Z(−1, 1).  Which of the following can be used to prove…

A: Given △XYZ is given with X(2, 0), Y(0, −2), and Z(−1, 1)

Q: az Find if yz – In z = x + y ax

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Q: 2.Prove that L (sinwt) %3D s2+w?

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Q: 1f itwas x25ect, yatunt prove Thut dy

A: Simple derivative

Q: Show that the following cosh 3 (0,0) r(3,5) x² y?. (10xdx +6ydy)

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Q: Let X and Y be independent and distributed as N(mu, 1). Is T=X-Y sufficient?

A: According to factorization theorem, if the likelihood function Lx,θ can be expressed in the form.…

Q: 27 dr = iex+ h where a, b> 0. Prove that

A: Prove that , ∫-∞∞e2xae3x+bdx=2π33a23b13

Q: Q/Use Definitien 13.4-1 +o prove that f(x,r}>x+y' is difterentialeat (o,0).

A: Given function is  fx,y=x2+y2

Q: Let BE Cnxn. If z" Bz = 0 for all z E C, then show that B = 0.

A: Given expression is

Q: Ôz Ôz If Z= tan"'(2) -= 0 show that : *-+ y ôx ôy

A: Let us consider function z=f(x,y) Where f is function of x,y. ∂z∂x represents partial derivative of…

Q: Evaluate So y? exy dA, where D 'is bounded by you, yit, x

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Q: Suponga P(Z,=K) = 2 Determine la distribucioñ de Zn. Ejercicio (DistrbugER del proceso de…

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Q: find the root of the fnmetion ーX FCx)= ē^ _ x which lies betwen (o %3D

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Q: 火2sin C&) for ダチo fcx) = { for x =0 show that Con tinods or not

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Q: (X), E(Y ) EXY), Cov(X, Y) , σχ, σχ and Py.

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Q: Then show that N(A) = R(AT)+ and N(AT) = R(A)+. %3D 11-1 02-3 -1 1-2 N(A) = N(AT) =

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Q: Solve for x in the figure * AJKL is isosceles with KJ = LJ. K x+3 X-1 J 2х- 5

A: Since, triangle JKL is isosceles, so, we have, KJ = LJ

Q: Q3. Let z, y be real numbers such that ry 1 and z #y. Prove that

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Q: Expand the function f(x) = tan x up to the first two non-zero terms in the Taylor's polyno- xn+1…

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.