37-1. Find the moment-generating function when the p.d.f. of X is defined by: 1 (a) S(x) = ; x = 1. 2, 3: (b) S(x) = 1, x = 5: 5 - x (e) S(x) = . x = 1, 2, 3. 4. 10

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: 5 Suppose X, is a geometric Brownian motion with u: 1. g? = 1. Given X, = 1. find the probability of…

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Q: 10. If E X=5' ,r=1,2,3,.., find M(t), the moment generating function of X, and the p.d.f. of X.

A: Given:  rth moment of random variable x  E(X^r)= 5^r   : r=0,1,2,..... To find moment generating…

Q: Let X ~ Poisson(λ). Derive the moment generating function of X and use that to find E(X3)

A: Solution: Let X~Poisson(λ) The probability distribution of X is  P(x)=e-λλxx!    x=0,1,2,3,..

Q: (a) Calculate the moment generating function for X. (b) Use the moment generating function to…

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Q: 2- An insulated rod of length 30 cm has its ends A and B kept at 20•C and 80•C respectively until…

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Q: Use the Laplace transform to solve the initial-value problem: [y " +5y' +4y=2 e*, y(0) =4, y '(0)…

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

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Q: 29. In Theorem 9.8, if f'(x o) = 0, no conclusion can be drawn about the equilibrium point xo of x'…

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Q: Let Mx(t) = 1/(1-t), t < 1 be the moment-generating function of a random variable X. Find the…

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Q: 9. Building upon Example 5.14, let X be a real-valued compound Poisson proce with Lévy measure v,…

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Q: Use the Laplace transform to solve the initial-value problem: [y" +3 y' +2 y= 3 e -3 x y(0) = -4, y'…

A: The given problem is to solve the initial value problem using the Laplace transform, we have to…

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: Example 17-4. Let X be distributed in the Poisson form with parameter 0. Show that only unbiased…

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

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Q: If the moment generating function of X is M(t)= 0.2+0.3(e^-t)+0.5(e^3t), then P(X>-1)=

A: Given that the Moment generating function of X is,

Q: Using Laplace transform to solve the IVP: y" - 5y = e", y(0) = 0, y'(0) = 0, then, we have ---…

A: As per guidelines i had solved the first question .kindly post another question separately.

Q: Suppose X and Y are two independent and identically distributed geometric random rariables. The pmd…

A: PMF of X is given by, P(X=x) = p(1-p)x-1 , x=1,2,3.... Now,  ⇒P(X≥x)= ∑t=x∞ P(X=t)= ∑t=x∞p(1-p)t-1 =…

Q: People arrive at a store based on a nonhomogeneous Poisson process with the following intensity…

A: Consider X be a random variable which follows a nonhomogeneous Poisson distribution indicates the…

Q: 10

A: Given DataMoment Generating function of X is

Q: Property 3: The auto correlation function evaluated at the origin (t= 0) will be its maximum…

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Q: 1.9.5. Let a random variable $X$ of the continuous type have a pdf $f(x)$ whose graph is symmetric…

A: The expectation of the random variable X-c can be represented as, EX-c=∫-∞∞x-cfx·dx The graph is…

Q: How do i find e(x), var(x) and e(x^3) using the moment generating function

A: Let us define the random variable X with moment generating function Mx(t).The moment generating…

Q: Suppose x, is the size of a population in generation t and in generation t + 1, X1 = f(x,), where…

A: Suppose x, is the size of a population in generation t and in generation t + 1,  xt+1 = f(x), where…

Q: 8] 5. Suppose that Y ~ I(n/2, B). (a) Use the method of moment-generating functions to show that W =…

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Q: if m1 =1 , m2 =1, c=2, k1 =3, k2 =2 and all initial conditions are zero, how can I solve this by…

A: Here, m1=1kg, m2=1 kg, c=2 Ns/m and k1=3 N/m, k2=2 N/m. The differential equations can be re-written…

Q: 2.7 a. The root mean-square (rms) bandwidth of a low-pass signal g(t) of finite energy is defined by…

A: (a)The given root mean square (rms) bandwidth of a low-pass signal g(t) of finite energy is defined…

Q: Suppose X1, X2, and X3 are independent and N(0.1)-distributed. Com- pute the moment generating…

A: Given function Y= X1X2+X1X3+X2X3 We have to calculate moment generating function

Q: 5. Suppose Xt is a geometric Brownian motion with u = 1,02 = 1. Given X1 = 1, find the probability…

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Q: 2. Define the p.m.f and give the values of u , o ? , and o when the moment generating function of X…

A: Given MGF is, M(t)=25+35et The given MGF is same as the MGF of the Bernoulli distribution,…

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

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Q: 1. Find the orthogonal trajectories of the family of curve a+3y2 = cy ,where c is an arbitrary…

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Q: a minimal realization of H(s). For any feedback gain realization for the corresponding Hƒ(s).

A: Given, (A, B) be a minimal realization of H(s).To prove: (A-BK, B) is a minimal realization for the…

Q: Prove that the random process {X(t)} with constant mean is mean-ergodic, T T 1 if | C(t,, t2) dt dt,…

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Q: 5. Suppose X; is a geometric Brownian motion with u = 1, o² = 1. Given X = 1, find the probability…

A: Answer: 0.098

Q: 1. A random variable, X, as moment-generating function M(t) = e, -00 <t< oo. (a) Find E[X]. (b) Find…

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Q: 6. Use Laplace transform to solve the initial value problem: y" - 2y' + 2y = et, y(0) = 0, y'(0) =…

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Q: 6. Use Laplace transforms to solve the initial value problems: (a) x" + 9x = 0; x(0) = 3, x'(0) = 4…

A: Given x''+9x=0, x0=3, x'0=4

Q: Use partial fractions to find the imverse Laplace transforms of the functions in Problems 13. F(s)…

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Q: 6. Use Laplace transforms to solve the initial value problems: (b) x" – x' – 2x = 0; x(0) = 0, x'(0)…

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

A: The solution are next step

Q: (a) Calculate the moment generating function for X. b) Use the moment generating function to…

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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: 1. Let X have the moment-generating function Mx (t) = (1– 2t)-r/2 , t< ½ (a) Find Var (-5X) +…

A: Given  X~χ(r)

Q: Theorem 7-13. µ' = E {X (X – 1) ... (X-r+ 1)} = P (). ,where u is the rth factorial moment of X. s=1

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Q: Use the Laplace transform to solve the given initial-value problem. y' +4y=e-4t, y(0) = 2 y(t) = 4t…

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Q: 11) If X be ar.v. from exponential distribution S(x) = de A>0, r20 Then the moment generating…

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Q: Which of the following graphs is the slope field for dx 12 -3-211. s 2 13 US 111-2-/35 1112 111²-111…

A: Here we have to solve the given differential equation and plot the solution

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: 3 Let X be a Poisson with parameter 1. Prove (step by step) that P(X < 4) = edr. 1 p³e¬²dx.

A: Given information: PX&lt;4=∫1∞16x3e-xdx