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Find r(A) and n(A) A = 1 -34 -1 9 -2 6 -6 -1 -10 -3 9 -6 -6 -3 3 -9 4 9 0 O a.r(A) = 1 n(A) = 4 b.r(A) = 4 n(A) = 1 cr(A) = 5 n(A) = 0 d.r(A) = 2 n(A) = 3 Oer(A) = 0 n(A) = 5 Of.r(A) = 3 n(A) = 2
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]
4. [5] Find a formula for the nth partial sum Sn of the series, as is done in Example 8 of chapter 11.2. Then, find the sum of the series or show that it diverges. Lk2 + 3k + 2 k=1
Compute the sign of the following permutations: (a) (1, 4, 3, 6, 7)(5, 8, 9, 10). (b) σ ∈ Sn, i 7→ n + 1 − i. (c) Show that this initial configuration of the 15 puzzle is not solvable 3 1 15 13 2 8 5 9 12 7 11 4 14 6 10 − (d) Suppose that (i, j) ∈ Sn is a transposition and that i < j. Find an expression (in terms of i and j...
PROBLEM 2 3k ut 3K 6 k FIND THE REACTIONS RA AND Rg. ALL MEMBERS ARE MADE OF ALUMINUM (EoxIo3 KsI),
Suppose X is a random variable with probability mass
function
Find k.
A. 9/80 B. 11/20 C. 9/20 D. 18/50 E. none of the preceding
f(x) = k if x = 0 3k if x = 1 11/20 if x = 3
how many moles of Sn 4+ are reduced to Sn 2+ if un culomb of
charge is transfered to the half cell in question
¿Cuántos moles de Snº: se reducen a Sn? si se transfiere un culombio de carga a la media celda en cuestión? Sn4+ + 2e = Sn2+ AE°= 0.139 Select one: a. 0.0045 b. 6.022x1023 C. 96,490 O d. 5.18x10-6 . e. 4.70x10-8 Clear my choice
(5) Let o be a k-cycle in Sn. (a) Prove that ok = id. (b) Prove that k is the smallest positive integer i such that oi = id. Thus, the order of a k-cycle in Sn is k.
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)
9 Let Xi, X2, ..., Xn be an independent trials process with normal density of mean 1 and variance 2. Find the moment generating function for (a) X (b) S2 =X1 + X2 . (c) Sn=X1+X2 + . . . + Xn. (d) An -Sn/n
9 Let Xi, X2, ..., Xn be an independent trials process with normal density of mean 1 and variance 2. Find the moment generating function for (a) X (b) S2 =X1 + X2 . (c)...