If X; derive the moment-generating function (mgf) of X?. Ν (μ, σ) :

Q: (S 3 Solve the following equations by Laplace transforms. dx + 3x = e-2t (a) dt given that x = 2…

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

Q: Solve the IVP using Laplace transforms. x'(t) = t?, x(0) = 4

A:

Q: If the moment-generating function of X is M(t)= e, then the moment-generating 3t function of Y=1+-X…

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Q: In each of the following find the pdf of Y. (a) Y = X? and fx(x)= 1, 0 < I< 1 (b) Y = - log X and X…

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Q: Solve the following Bernoulli's D.E.: dy 3 „y = x*y3 1 %3D dx

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Q: Observations on the yicld of a chemical reaction taken at various temperatures were recorded as…

A: Given information: Given the yield of a chemical reaction taken at various temperatures as x(C0)…

Q: the moment-generating function of X is M(t)= et, then the moment-generating function of Y=1+. 3

A:

Q: xsin tx -dx [Ans : Te¯ª"] -at 5. * (x² +a³)'

A: ∫-∞∞x sin txx2+a2dx To Find: Evaluate using Laplace Transform:

Q: In lns Ing Ss H.w X. 2 dy dx Drad ad Evaluade the Aner expressd by be above ndagral

A: given       ∫0lnln8∫y=exln8exeydydx=

Q: Quest The moment generating function of X is given by Mx() = exp(2e - 2} and that of Y by Myt) = (e…

A:

Q: 3 Solve the following equations by Laplace transforms. dx (a) + 3x = e-2t dt given that x = 2 when t…

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Q: 3t If the moment-generating function of X is M(t) = e, then the moment-generating function of Y=1+-X…

A: The provided information is: The moment generating function of X is given blown:

Q: Suppose Y is the number of phone calls to an office during certain time with the moment generating…

A:

Q: 4.) Suppose X has moment generating function MX(t) = 0.3e−t + 0.1 + 0.1et + 0.2e2t + 0.3e3t. What is…

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

Q: The equation implicitly defines as a function of t. Find dr dt da dt 11 2 cos (6 x) = -8

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Q: 11

A: Condition:

Q: Derive the MGF and factorial moment generating function of X using this given PMF:

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Q: a) Find the moment generating function of X. b) Use the MGF to find E(X) and Var(X).

A: Let , pdf of a continuous random variable is ,  = 0 ; otherwise Our aim is to find the following :…

Q: Solve the following initial value problem by using Laplace transform. y" – 2y/ + y = 0, y(0) = 4,…

A: The differential equation can be rewritten as below:d2ydx2-2dydx+y = 0 where y(0)=4 and dydxat 0 =…

Q: Sy" + y = 8(t – 27)cost, 2т)сost, у (0) 3 0, у/(0) — 1

A: The solution is given as

Q: Let SINGLEDFA = { | M is a DFA and for all s e L(M),|s| = 1}. Show that SINGLEDFA is decidable.

A: Detailed explanation mentioned below.

Q: (x' Log, x dx O For what values of p does al converge?

A: SOLUTION-

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

A: According to question, dPdt = dBdt-dDdt

Q: use the Laplace transform to solve the given initial-value problem. dy di -Y= 1 P. | У(0)-0

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Q: Solve the following initial value problems by Laplace transform technique

A: We have given a differential equation ,  y'' + 2y' + 5y = 50t - 100   ,  y2 = -4  , y'2 = 14 This is…

Q: Calculate coefficient of Q.D. and bowley 's coefficient of skewers from the data given below:…

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Q: Use the Laplace transform to solve the following initial value problem: "+ 3д' %3 0, г(0) — 8, 2'(0)…

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Q: ind E(X) and V(X) for 28(t) = 0.4e2t +0.6e¬3t. random variable X whose moment-generating function i…

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

Q: Prove that coshz =log ztv= {Hint : cosh z =e} 2.

A: Use the hint and prove this.

Q: f substance B, in milligrams, left after t years, given that the initial quar

A: Option of part c is A.

Q: Suppose X has moment generating function M (t) = est Then E (X) = 1-2t

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Q: Let X ~ T(a, B). If E(X) = aß and E(X²) = aß² + a² ß². If â = X, find the method of B moments…

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Q: 2t If X has moment generating function M (t) = the E (X) is equal to 1+3t

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Q: 1. Calculate the second moments in time and frequency around time zero and frequency zero,…

A: Given: The function st=e-t22   To calculate: The second moments in time and frequency around time…

Q: If X is an exponential r.v. with parameter 5, identify the r.v. 10X

A: Introduction: The random variable X has an exponential probability distribution with parameter, λ =…

Q: Use the Laplace transform and its inverse to solve the following initial-value problems: a) y = 2et;…

A: To solve the given initial-value problem using the Laplace transform and its inverse. a)…

Q: Solve the following IVP using Laplace Transform y' − 2y = 1 − t  ;  y(0) = 4

A: The Laplace transform is given as: y'−2y=1−t,y0=4Taking the laplace trasform on both…

Q: 2. Evaluate the following integral: dy dx

A: We need to reverse the order of integration to calculate given double integral

Q: If X ~ gamma(r, 1), show that the moment generating function of is given by if t < A. Mx(t) = { ()",…

A: Given, Mxt=λλ-tr As we know that, Ex=Mx'0Ex2=Mx''0 Now, Mx't=ddtλλ-tr=rλrλ-tr+1

Q: Compute the value of the following integral: ∞ (t) cos() 8 (t-1)dt ∞ 2 where 8(t) is the unit…

A: According to the definition ∫f(x)dx=F(x)+C, where dFdx=f(x). A delta function is defined as δ(t-a)=0…

Q: If the moment-generating function of X is a. M(t)=(1–21)"", 1 < ½, Find the p.d.f of X hence use it…

A:

Q: Ex. 130. Given the s-domain signal: F(s) ( 7 s^2 + Determine the steady state value of f(t) using…

A: we have Fs=7s2+3s+9s3+10s2+13s limt→∞ft=lims→0sFs

Q: Use Laplace Transform to solve the following initial- value problem: (2) dx + xy 4x y(0) = 0, ỳ(0) =…

A: Given, dydx+xy=4x , y(0)=0 ,y'(0)=2 Taking Laplace Tranform throughout the given Differential…

Q: 6. The energy stored 'W' in an inductor is given by (t2 - 21 -2t dt W =

A: The solution are next step

Q: Solution the following initial Value problem using the laplace transform y"+ 4y=4t, ylo)=1 and…

A: Given the initial value problem      y''+4y = 4t, y(0)=1, y'(0)=5 Solve it using Laplace transform.

Q: Given this periodic function: f(t) =1 from 0<t<a and f(t) = 0 from a <t< 2a Solve for the Laplace…

A: Please find attachment for the details solution

Q: 3 Solve the following equations by Laplace transforms. dx (a) + 3x = e-2t given that x = 2 when t =…

A:

Q: Suppose Y is the number of phone calls to an office during certain time with the moment generating…

A: We have to find thrid moment about zero for given moment generating function.

Q: Prove that by Gamma Function pit +e e-st dt %3D s2 +1

A: Gamma Function: The gamma function, denoted by is denoted by which is convergent for Some…

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.