Here , we see that both LHS and RHS are same...
Any query then comment below...
a. 1 4. Let Sn =EX=1 Show that In(n+1) < Sn S 1+In n b. Show that {an} = {Sn - In n} Show that sequence {an} converges C.
6. (i) Prove the recursion Sn+1,k+1 = Li () Sn-i,k for the Stirling numbers of the second kind. [3] (ii) Deduce that Sn+1,6+1 = [: (?) Si,k. [1]
(b) Show that if lim sn oo and lim tn > -oo, then lim(sn + tn) 1 +oo.
Problem 5.4 (10 points) Let (Sn)n-01. be a simple, symmetric random walk with starting value So-s e R. (a) Show that ES for alln0 b) Show that ElSn+1 Sn] Sn for 0. (c)Suppose that (Sn)n-0,12,. . denotes the profit and loss from $1 bets of a gambler with initial capital So-s who is repeatedly playing a fair game with 50% chances to win or lose her stake. What are the interpretations of the results in (a) and (b)?
Problem 5.4...
Sn is permutation group
(6) For (i ik) E Sn write down its inverse.
3. (12 points) Consider the following sum: n Sn = {(i + 1)(i +2) i=0 (a) Use properties of summations to find a closed form expression for Sn. Simplify your answer into a polynomial with rational coefficients. Show your work, and clearly indicate your final answer. (b) Use weak induction to prove that your closed form works for every integer n > 0. Make sure you include all three parts, and label them appropriately!
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cell Sn/Sn (IV) ion- Ni/Ni (II) ion will have electromotive
force.
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will post the whole page but the question i need is #4.
EXPERIMENT 24 PRE-LABORATORY QUESTIONS Define the following: salt bridge, anode, cathode, electrolytic cell. 1. Using Table 24.1, answer the following questions. (a) Which half-cell will be the anode in a cell composed of Al/APion or Mg/Mg2tion half cell couples. Briefly explain. (b) Sketch a diagram of the cell that would be formed by connecting the...
Exercise 5.22. Let (Xn)nel be a sequence of i.i.d. Poisson(a) RVs. Let Sn-X1++Xn (i) Let Zn-(Sn-nA)/Vm. Show that as n-, oo, Zn converges to the standard normal RV Z ~ N(0,1) in distribution (ii) Conclude that if Yn~Poisson(nX), then ii) Fromii) deduce that we have the following approximation which becomes more accurate as noo.
6. Let si = 4 and sn +1 (sn +-) for n > 0. Prove lim n→oo sn exists and find limn-oo Sn. (Hint: First use induction to show sn 2 2 and the.show (sn) is decreasing)
Suppose that and are Cauchy sequences. Show that the sequence is also Cauchy. Sn We were unable to transcribe this image(Sn-tn