eAt = I + At + A²2 + + 2! k! k=0 o compute eAt and e-At (; ) 1 A = 0 2 eAt = e-At Need Help? Read It

Q: e that the test is inconclusive: k 1. Lk=0 2k+1 k 2. Σ-2 k%32 Ink

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Q: 8. Find the antiderivative of (12x²)ex³ O 4e+³ 4eX +C O (4x³)e+³ +C O None of these Cannot be found

A: Let's find antiderivative of given function.

Q: 49. f(x) = alst %3D n=0 Selet ai 50. f(x) = 2 (-1)+1(x – 5)n n5" n=1 * (- 1)n+1(x – 1)"+1

A: f'(x)=∑n=1∞ (-1)n+1n(x-5)n-1n5n      =∑n=1∞ (-1)n+1(x-5)n-15n Apply the ratio test to check the…

Q: L{t + et} =+ I. L{t + e3t} = = 1 %3D II. S-3 52 5-3 L{t + e*} =+ L{t + e#} = - III. IV. S+3 52 543

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Q: f(x) = ao + a,x + azx² + azx³ € R[x] polinomu için –2 e R, f(x) polinomunun bir kökü ise x+2 e R[x]…

A: As ℝ is a ring of real numbers. So ℝ[x] is the polynomial ring that contains all polynomials in x…

Q: a21 is the susceptible residents becoming infected in day 1 = 0.4 a22 is the residents remaining…

A: Given, In a dormitory there was a common cold epidemic. Each day 40% of the dorm residents became…

Q: 0.6- |Natural input Z Reduced input 0.4- 0.2- roportion eaten (dry mass) HRE

A: The given diagram is a multiple bar graph which shows the proportion of dietary consumption of…

Q: 23 4- [fe** dycdx ans :(e' - e' )(e² – e') 12

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Q: 13) If it is known that -6 L{e% f(t}} s2 – 14s + 40 with certainty it can be assured that: a) f(t) =…

A: We will first find F(s) the using inverse Laplace we will find f(t) We know…

Q: If x¨ + x˙ − 6x = e ^−t, with x (0) = x˙ (0) = 0, what is X (s)?

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Q: A chemical supply company currently has in stock 100-lb of a certain chemical, which it sells to…

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Q: 3. A machine has n components, the lifetimes of which are independent. However the whole machine…

A: Since you have asked multiple question, according to our guidelines we will solve the first question…

Q: 1 Prove the inequality: EP, log(-)<P, log(- P i=1 i=1 N N with the constraint: EP, =EQ, = 1 i=1 i=1…

A: The given constraint is  ∑Pii=1N=∑Qi=1i=1N To prove that ∑n=1NPi log 1Pi≤∑n=1NPi log 1Qi

Q: 4) Suppose S has pmf given below. Find E[(S- 1),]. k 1 2 3 P(S=k) 0.1 0.2 0.4 0.3

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Q: 4. y= 5e, y-s+ax-3x between x-0 and x=1 about y= -3

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Q: 100 e of f (s) = %3D s (s+2)2(s+3)

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Q: b) Show that MsE(S²) = (п-1)* c) You are given another estimator of o? which is T² = = (X; – X)² i=1…

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Q: Seaet =1+ e* + e3x + e(n+1)x enx +esx. n! sx € (0,e*) | ... 2 (п + 1)!"

A: we know that ex=1+x+x22!+x33!+........................+xnn!                      ..1

Q: Estimate the value of E-2 (1/(n² + 4)) to within 0.1 of its exact value.

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Q: * السؤال .13 L[u(t – 4) (r²6' – 16 6')] = - %3D O n Ge-d" (금 + ) -4s O 6'e * (-In 6) ). 2 (s-In 6)…

A: Lapalace transform satisfies linearity property, La·ft+b·gt=a·Lft+b·Lgt. By laplace transform table…

Q: (b) Determine e so that п п c£[(x; - X;)² i=l j=1 is an unbiased estimator of o². s2 ogunl to

A: 6. From the given information, X1,.....,Xn~f be an iid random sample with mean μ and variance σ2. a)…

Q: 2. Let P: C(0, 1]C(0, 1] be given by Pp "- e. Compute dP(x). Be sure to justify your calculations.

A: Given: The given function is  P:C20,1→0,1 given by pφ=φ''-eφ

Q: Suppose you have a model: wage = a, + azeduc; + «21Q; + azexper + a,DM, + a,DF + a,DE, + € where:…

A: Given information: The multiple linear regression model is given.

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

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Q: a. b. INGIN IN C. + S (S-1)² e35 + 5-1 e-3s S 5+1 d. None of the above L{2+ (t-3)et-3 U(t-3)] = +

A: Consider:  L2+t-3et-3 Ut-3=L2+Lt-3et-3 Ut-3 Now, L2=2L1=2×1s                      since L1=2s So,…

Q: | Va(In(x))° dr (ax) 1.

A: We find the integration by substitution.

Q: (6) Let x1, -- ,X1o N(u, o2), where µ e R and o > 0 are unknown parameters. Consider the following…

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Q: - S e-ttat1-1 dt a # 1 a '0

A: We use the definition of the Gamma Function to solve the given question.

Q: The mortality function for (90) is given by { min(X,Y) H (90 +t) 10 max(X,Y) 0<t < 5 t 2 5 10 where…

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Q: 14. s(1 + VE)dt +tVE ds = 0; when t = 1,s = 1

A: Firstly , separate the given differential equation and after that integrate both sides.

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

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

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Q: Let X1, X2,..., X, be i.i.d N(0, 1). e most powerful test for testing H : 0 = 0 against K > 0. ower…

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

Q: az given that yz*+x2z3 = eyz ax

A: H

Q: 4. In one model of the changing population P(t) of a community, it is assumed -, where and are the…

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Q: Suppose X~N(148,8), and Z~N(0,1). Then x = 143, is equivalent to z = ______. (Round your answer to 2…

A: Given information  X ~N(148,8) Population Mean (µ) = 148 Standard Deviation(σ) = 8 X= 143

Q: B/let Flx)=[X]-X,x E(-2,2).which valuesof x o E(X) continuaus?

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Q: a'(t) = -x(t – 1), x(t) = 1 on [-1,0], is given by 1(t) = E(-1)* t – (k – 1))* k! for n-1<t <n, k=0

A: As per the question we are given the following first order time varient differential equation :…

Q: It is known that mortality follows De Moivre's law. If Var (T(50)) = 192 , calculate w Instruction:…

A: According to De Moivre's law, if sx=1-xw then Tx follows uniform distribution in the interval 0,w-x.…

Q: L %3D e2t e-3s-6 (s+2)? O e6-3s ( 1 3 + S+2 (s+2)2 O e-3s (s+2)2 1 3 s+2 O e2-3* ( +) 1 (s+2)2 s+2 O…

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Q: (3) In one model of the changing population P(t) of a community it is assumed that dP dB dD dt dt dt…

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Q: 8) F(s)=³-ks² 2 Ans. f(1) =2(e"-1)-! k

A: Solve the following

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

A: Answer: For the given data,

Q: 9. Find the antiderivative of each of the following:

A: We are solving the first three subparts and for the remaining subpart post the question again and…

Q: %3D in Fin d E(S an d Var(s)

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Q: n +1 5n An bn n + 2' 4n2 – 3' { 400/n -1/(400n2) n even { Į 7 n/(1+n²) 1 901 п оdd Cn dn

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Q: S 1 {1- | neN} n inf S min S max S sup S

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.