Suppose that an >0 and bn >0 for all n2N (N an integer). If lim = , what can you conclude about the convergence of an? A. a, diverges if by diverges, and an converges if bn converges. an diverges if by diverges. c. a, converges if be converges. OD. The convergence of an cannot be determined.
Let n > 1, and let S = {1, 2, 3}" (the cartesian product of {1,2,3} n times). (a) What is Sl? Give a brief explanation. (b) For 0 <k <n, let T be the set of all elements of S with exactly k occurrences of 3's. Determine |Tx I, and prove it using a bijection. In your solution, you need to define a set Ax that involves subsets and/or cartesian products with known cardinalities. Then clearly define your bijection...
HW: Show that the series __, an n=0 converges whenever ſal < 1, and diverges whenever al > 0.
PLEASE HELP WITH PROOF!! 8. Let an > 0 for all n in 1. Show that if an converges, then Ĉ vanın converges. [Hint: Expand [van - (1/n)]2.) N =
Let X1...Xn be observations such that E(Xi)=u, Var(Xi)=02, and li – j] = 1 Cov(Xị,X;) = {pos, li - j| > 1. Let X and S2 be the sample mean and variance, respectively. a. Show that X is a consistent estimator for u. b. Is S2 unbiased for 02? Justify. - c. Show that S2 is asymptotically unbiased for 02.
Soru 2. Suppose the series Ebox" converges for (x1<4. Select all that applies n=0 Yanıtınız: (-1)"b,4" converges n=0 6" M8 M 0,4" converges. n=0 61 6,6"4" diverges. n=0 00 (-1)"b,4" diverges. n=0 boxn+1 n=0 n +1 È converges for all |x<4 nb bmxn-1 converges for |x|<4 n=1 Testi duraklat Geri Sonraki
(1) Suppose f :(M, d) + (N,0) is not uniformly continuous. Show that there exist an a > 0 and sequences (Xn) and (yn) in M such that d(Ion, yn) < and o(f(xn), f(n)) > € VnE N. (Hint: Negation of the definition of uniform continuity.)
Exercise 7. Let X be a standard normal random variable. Prove that for any integer n > 0, ELY?"] = 1207) and E[x2n+] = 0.
ALGORITHM X(A[0..n - 1]) // Input: A contains n real numbers for it 0 to n - 2 do for jt i +1 to n - 1 do if Aj] > A[i] swap A[i] and A[j] 1. What does this algorithm compute? 2. What is the basic operation? 3. How many times is the basic operation executed? 4. What is the efficiency class of this algorithm?
Please prove this, thanks! 2. Let {xn n21 be a sequence in R such that all n > 0. If ( lim supra) . (lim supー) = 1 Tn (here we already assume both factors are finite), prove that converges.