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 to calculate i. Е(X), ii. Var(X).

Q: dt converges. There is no value of r such that (3t)-" 14.

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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: 1+e-* Show that dr diverges.

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Q: tinuous at t= 0, it is continuous at every other point. 3 If the autocorrelation function R(t) of a…

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Q: dx converges. Determine the values of p for which

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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: the Following is divergent

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Q: Find the radius of convergence for: (- 1)"x" Vn + 7 TL=1

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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: Find the Tians Farm F(s) = "suy (27>1>0) (1 – s)(1 – e **) 3) f(1) = e',

A: Given problem:- Find laplace transformation of f(t) =et (0&lt;t&lt;2π)

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

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Q: Suppose that Tis to be found from the formula T=x(ey + e -), where x and y are found to be 2 and In…

A: Suppose that T is to be found from the formulaT=xey+e-y where x and y are found to be 2 and ln2 with…

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: 11

A: Condition:

Q: dx converges and, if so, to what. 49. Determine whether J = | E/1* I-

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Q: By using the substitution t² determine the convergence of = S ∞ dx (x+1)√√x*

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Q: Find the radius of convergence for: Σ (- 1)"2" n=1 Vn+4

A: use the formula for radius of convergence for the

Q: The number of deaths among members of the U.S. Navy in the first 3 months of the 1918 influenza…

A: (a) Numerical estimation of N with increase in t.

Q: Find the radius of convergence for: (– 1)"z" 00 n=1 Vn + 8

A: Given series is ∑n=1∞-1nxnn+8. We have , 1R=limn→∞an1n=limn→∞an+1an, where R is the radius of…

Q: a) For which values of x does f(x) =E n=0 converge and for which values ofx does it diverge? b) When…

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Q: The approximation of the root a of the fanction f(x) -* -Sa +9x +3 in the interval (4,6]accurate to…

A: Substitute 4.5 and 4.6 for x in the function fx=x4-5x3+9x+3 and simplify, to get the values of f(x0)…

Q: 51. For which values of a does eax dx converge?

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Q: f fn → ƒ uniformly and the functions fn have only jump discon- sinuities, prove that f has only jump…

A: Here we use epsilon delta proof

Q: There is one male baby seal for every nine female baby seals. Let X be the number of male baby seals…

A: Let p=P(male baby seal) = 1/9 Here n=5 Note that X follows a Binomial distribution with n=5 and…

Q: Prove that sina de converges but not absolutely for 0 < p < 1. XP

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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: Show that the series n=0 xn cos(nx) x² +n³ + 1 defines a differentiable function g(x) for x in [-1,…

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Q: 00 6n–1 Зп+2 1 Apply the nth term divergence test to conclude if E converges or diverges.

A: The divergence of a series can be found using the nth term test. Consider the series . Let . If…

Q: 4. Determine whether the function g(x) = roo sin²x converges or diverges by comparing it to f(x)…

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Q: Suppose that X and Y are independent rv's with moment generating functions M(t) and My(t),…

A: If X and Y are independent random variable and Z = X + Y then m.g.f of Z is equal to the product of…

Q: Determine whether

A: Solution: Consider the given integral equation: J = ∫-11dxx1/3 Since the given integrand is defined…

Q: Is xo is an ordinary point of the ODE? If so expand p Find a minimum value for the radius of…

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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: 2 Q/if the function fc)=ĕ is not Continuous at T where =TIL x<T foint the fourier Scries of fcxeě is…

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Q: CoS“ n In n а. n2 n³ n=1

A: Solution: a) ∑n=1∞cos2(n)n2+ln (n)n3

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

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Q: Suppose f(x) > 0 and g(x) > 0 and that | f(x)dx diverges. If f(x) > g(x), what can we conclude about…

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Q: By using the substitution x = t² determine the convergence of d.x [ (x + 1)√x

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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: Find Residues by using Lourent's Series f(²)=3/²2 at Z₂ = FL

A: Given f(z) = zz2 - 1

Q: -4 After evaluation, Jo dx tends to be 0 x2-9 A. convergent B. divergent C. insurgent D. allegiant

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Q: If E, 2"an converges and E o(-1)"2"an diverges, then the radius of conver- gence of o anx" is 2.

A: According to the given information, Suppose,

Q: b) Use the Comparison Theorem with f(x) = - to show whether , g(x)dx is convergent or divergent.

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Q: Determine the values of p for which f(x)da converges where f(x) = = 1-e-z TP

A: Here, in the question for what value of p the integral is convergent. The simple improper integral…

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: Which of the following is an advantage of the Newton-Raphson Method? O root jumping requires only 1…

A: We have to find from the given options which is the advantage of Newton Raphson method.

Q: Find the radius of convergence for: – 1)"x" Σ Vn + 5 n n=1

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