et H={Φ∈Sn | Φ(n)=n}. Find index of H in Sn.

Q: Let X Gamma(a, B). Prove that for any positive integer n > 1, E(X") = [(a +n– 1)(a+n – 2)..-a]3".

A: It is given in the question that X~Gammaα,β then we have to prove that for any positive integer n≥1.…

Q: The Maclaurin expansion of f (x) = e-5x is +00 5"x" (-1)"5"x" n! n=0 n! n=0 as above O as above +00…

A: The Maclaurin expansion of f(x) is given by f(x) = f(0)  + xf'(0)1! + x2f''(0)2!+ x3f'''(0)3! + ...…

Q: A. let w-e te Find W2

A: We can solve this using u/v rule

Q: Find k such that 2x = ekx for all x.

A: To find k 2x=ekx

Q: Which of the following statements involving sigma notation is always true? η η η Α) E (ak bR) = E…

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Q: 1 The function f (x) has a Maclaurin expansion. x (х-1) True False

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Q: Let T(N) = 1. T(floor (N/3)) + 1 and 7(1) = T(2) Prove by induction that T(N) ≤ log N + 1 for all N…

A: Given: TN=TfloorN3+1 T1=T2=1   To Prove: TN≤log3N+1 for all N≥1, using induction.

Q: Let Zn be the size of the nth generation in a GW process with Zo = 1, E(Z¡) = µ. Show that E(Z„Zm) =…

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Q: LetX ∼ P oisson(λ). Prove that E[X(X −1)] = λ 2 and use this result to show that var(X) = λ.

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Q: Let X - Poisson(a). Show that E X(X - 1)(X- 2).… (X – k)] = ak+1

A: We are given that: X~Poissonαfx=e-ααxx!         x=0, 1, 2,....

Q: The characteristic of Z5[x]/ is O 3 5

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Q: Find the constant term in the expansion

A: We have to solve the problem

Q: Find all values of x such that ΣΗ converges. n! n=1

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Q: Use the selected values of a linear fuetion g(x) in the table and the equation h(x) shown below to…

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Q: Prove that for the gamma function [(x) = ftx-¹e-tdt that for n a positive integer then I(n) = (n-1)!

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Q: Let n be a positive integer. The coefficient of x°y° in the expansion of (1+ xy+ y²)' equals

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Q: For each n E N, consider xn n == X with x ER+. Define the sequence {gn} by 1 +2' 8n(x) = f(xn) (a)…

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Q: Find the elements (a, b) of G of order 2. O Show that G has no element of order 3.

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Q: Find an example of fn → f in measure, but for every x, fn(x) does not converge to f(x).

A: We have to find an example of fn→f in measure, but for every x, fn(x) does not converge to f(x).

Q: 2. Find the value of the Euler phi-function at each of these integers- e) 10! b) 256 d) 2.3-5-7-11-…

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Q: (a) Prove that (2x + 2) > 1 for all x > 0. (b) Let so > 0, and sn+1= } (2s, + ) for all n > 0. Prove…

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Q: Prove that for every v = (x, y) E R? there exists a sequence v, = (xn, Yn) € R2, where rn, Yn are…

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Q: Find the odd and even half range expansion, f(t) Lt KIN RIN

A: Given:   To find: The odd and even half range expansion

Q: 7. (a) Find all the values of z such that e = 1+ i.

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Q: The function 5x+1 f(x) 1-In (x³ +e) has a Maclaurin Expansion O false O true

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Q: Given: a, = In(n + 1) – In(n) for n e N Determine if the following is convergent or divergent. (a)…

A: Given that an =ln(n+1) - ln(n) We have to find whether the sequence ann=1∞  is convergent or not. A…

Q: Find the limit of s(n) as n o. 1n(n + 1) | s(n) n2 8

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Q: x" En=o n! Σ converges absolutely for all x

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Q: Let Y Poisson(A), with A > 0. Then, show that Tchebysheff's inequality gives P (0 1

A: Introduction: Suppose X is a random variable with expectation, μ and standard deviation, σ. Then,…

Q: Show that if X ~ Poisson(A), then there exists m ER such that pX (k) is increasing for ksm, and…

A: A discrete random variable X has a Poisson distribution, with parameter 0}">{\displaystyle…

Q: Suppose f"(x) = N (h) + a,h + azh2 + azh + -. The value of N½(h) using Richardson's extrapolation…

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Q: Prove the following combinatorial identities (algebraically): (") = Eo ("*) 1) ("") = E, () (") 2)

A: We have to prove thatm+n+1n=∑k=0nm+knProof⇒ As L.H.S is number of subsets {1,....,n+m+1} of size n…

Q: Let x1 O and xn+1 x+1 2 Show that (x,n) converges and find its limit.

A: It is given that  x1=0 and xn+1=xn2+12. Let xn+1=ϕ(xn)=xn2+12 By fixed point iteration method…

Q: The set of all open le ft rays together uwith all open right rays for the usual topo log y on R is…

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Q: Find the smallest integer in the given set a.{ xϵ Z f x > 0 and x = 4s + 6t for some s, t in Z }

A: Consider the equation: x=4s+6t……1   where: x, s, t∈ℤ and x>0

Q: k en(k) 大=Z

A:

Q: Given a sequence x(n) for 0sn<3, where x(0) = 1, x(1) = 1, x(2) = -1, and x(3) = 0, compute its DFT…

A: Given sequence x(n) for 0≤n≤3 isx(0)=1,x1=1,x2=-1,x3=0The DFT x(k) is computed as shown below

Q: 2. Let E CR. Prove E' is closed. 3. Let E CR. Prove ro € E' iff for every e > 0, N(xo, e) contains…

A: #2- For a subset E of R, E' denotes the set of all limit points of of E.

Q: 17) Draw the graph of a function K(m), such that S К (т) dm о

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Q: Find the joint characteristic function of X and Y if SxY (x, y) = 1 exp

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Q: (e) Choose {X,}"-1 from [0, 1]. Let p, be the probability that X; + X;+1 < 1 for all i € {1,2, ., n…

A: Given thatXi for i = 1,2,3,...,n are distributed uniformly from 0,1. Let us consider two random…

Q: Suppose f(x) = N(h) + a,h2 + azh + agh +.. %3D The value of N,(h) using Richardson's extrapolation…

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Q: For each n EN, consider xn = n with x ER+. Define the sequence {gn} by XER+. x 1 Xn 8n(x) = f(xn):…

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Q: Let f(x) = En-0 n, > 1 Compute E2(f(k) – 1) using doubly indexed sequences.

A: Consider the provided question, In your problem n=0 to ∞ is not define at n=0fx=∑n=1∞1nx,     x&gt;1…

Q: Exercise 6.12. Let E = {1/k: ke N} CR. Prove that a is a limit point of E if and only if a = 0. In…

A: