Q: 3.3 Prove that E does not converge uniformly k! k=0 on R.
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Q: 4. The total number of the accessible microscopic states of the Boltzmann gas, with energy E and…
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Q: Show that the Stein operator for Poisson P(Y = k) = is Tf(r) = Af(k + 1) – kf(k).
A: Given information: The Stein operator for Poisson P(Y = k) = λk/k! is Tµf(x) = λf(k + 1) – kf(k).
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A: Given that
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A: Given Information: Xt:t∈T be a time series for any t1 and t2.
Q: Let f(x) = Eoe > 1 Compute E2(f(k) – 1) using doubly indexed sequences.
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Q: Y thenumber of Limits of. E -63? gontric k series Skz Ak=7 B に2 6 Ok26 No if the above.
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Q: Let S= (-2, 3]U(4,5). The largest possible value of E SU such that Select one:
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Q: 1. Let X~Poisson(a). Show that E[X(X – 1)(X – 2) ... (X – k)] = ak+1 -
A: Solution
Q: 3.19 Suppose if r = 0, f(x) = {-1)" if r E n+1' n where n E N. Prove: f € R[0, 1], even though f has…
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Q: If x is a lower bound for S in R then x must be unique..
A: If x is a lower bound for S in R then x must be unique.
Q: 11. Let S= {| -2 }. Show that u= E span S. 1 2
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Q: 13.D. Show that, if we define fn on R by fa (x) 1+ n?x? then (fn) converges on R.
A: givenfn(x)=nx1+n2x2dividing numerator and denominator by x2fn(x)=nxx21+n2x2x2
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Q: ssume X ∼ Poisson(r), where r > 0. Prove that E(X) = r.
A: We have given that X ~ Poisson(r), where r > 0.
Q: a) Show by example that E( an /b.) may diverge even thagh E an and E bn converge and no b, equals 0.
A: Since solve the first question for you. If youwant any specific question to be solved then please…
Q: Example Suppose that Y Poisson(X) and consider testing Ho: A = A ild against H₁ A Av. solve it now
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Q: Let Sn=Vn. Find an and show that an O but that Sn=ER=1@k diverges. ->
A: Solution:-
Q: see the equation as attached here
A: Solution:Given 0<an≤bn and∑n=1∞an divergesTo prove:∑n=1∞bn diverges
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Q: Give a recursive definition (with initial condition(s)) of (an) where (n = 1, 2, 3, . . . )
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Q: *show tht the fanetion fW=$- satify The by PotheseI of Rolshe oren- on [0,4]
A: For the solution follow the next step.
Q: determine the radius and convergence of E n=1 5xn/3n2
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Q: 5. Prove that . Hint: Compute e-' from the continued frac e - 1 1 + 2 + 3 + ·…. tion for et given in…
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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: 7. Let x₁ = a > 0 and Xn+1 = x + 1/x,, for n E N. Determine whether (x,) converges or diverges.
A: Q7 asked and answered.
Q: Does E 8. k=1 In(ek41) converge or diverge?
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Q: 1+! A) S diverges B) S converges absolutely n=1 1/2
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Q: If {X(t)} is a Poisson process, prove that n - r S P{X(s) = r/X(t) = n} = nC, where s<t %3D %3D
A:
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<4=∫1∞16x3e-xdx
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