show that if ch[k-n], h[k] > = Ži h*[kn] h[k] = Str], then I Herita, 1...
. km m2k 1. Please show that the mean is * k > 1, and variance is k-1 (k-1)2(k-2)' for Pareto distribution. Please also show that the Pareto distribution approaches δ(x-m) as k → 00,
I. Let {X n\ be a sequence of random variables wit h E(X,-? for n- 7n exists a C > 0 such that for n 1,2, 3,.. Show that X is cons istent for ?
b) Show that the following claim holds when for all n > 1 n (424) > n(n+1)(n+2) i= 1
2) (3 pts) Use mathematical induction to show that when n is an exact power of 2, the solution of the recurrence 2, ifn=2 T(n) =127G)+n, ifn=2.for k > 1 ISI(72) = n lg n.
1. Show that, for every n > 1: n ka n(n + 1)(2n +1) 6 k=1
6. Use Mathematical Induction to show that (21 - 1)(2i+1) n for all integers n > 1. 2n +1 (5 marks) i=1
Question 4 Find i(t) for t >0 for the circuit below. 4Ω 12 V 5 H 3 A
5. Evaluate the limit: lim expn n! n>00
Using the pseudocode answer these questions Algorithm 1 CS317FinalAlgorithm (A[O..n-1]) ito while i<n - 2 do if A[i]A[i+1] > A[i+2) then return i it i+1 return -1 4. Calculate how many times the comparison A[i]A[i+1] > A[i+2] is done for a worst-case input of size n. Show your work. 5. Calculate how many times the comparison A[i]A[i+1] > A[i+2] is done for a best-case input of size n. Show your work.
Let F be a field of characteristic p > 0. Show that f = t4 +1 € F[t] is not irreducible. Let K be a splitting field of f over F. Determine which finite field F must contain so that K = F.