In this proof below, replace events with events. For
example, if there is , replace it with
.
If there is , replace it with
and so on.
6. Show that for any sequence of events (F)y-1
6. Show that for any sequence of events (F)-1 PPF(n-1).
For a probability space (Ω,F, P. ifB. Be' . . . is a sequence of events such that Ση i P(Bk) 〉 n ї. show that Pîne i Bk) 〉 0
Let f: R"R be the function TL Σ Ι.rlp. f(z) where 1 < p. Show that the conjugate is where 1/p+1/g-1 Let f: R"R be the function TL Σ Ι.rlp. f(z) where 1
Put the leyers in chronological order from yongest to oldest. I I 6. Sequence of Events A. Indined sequence Chronological Order nnest 12 and 10 onsups iIsctwen rock Isxies and D.Ignevus intrusion asa E. Meamophic in ihe Colorado Islatra". TİK' major rock labeled be letters, each representing a Igneous fntnision,-granite G. Ianecis intrusion-pranine H. Volcanic cinder cone I. Aluvial fan J. Lava fhow K. Erossonal surlace shown in alpbaecal, not chronolog cal, order in the adiacent column Study the diagram...
6. Show that if A1, A2, ... is an expanding sequence of events, that is, AC A₂C...... then P(ALU AQU....) = lim P(An). 1-00
Time series analysis 1. (a) Use Euler's identity e¡θ-cos θ + i sin θ to prove that sin θ=-(eiO , 2i (b) Use the identities above and the formula for the sum of a geometric series to prove that if n is an integer and j E 1,2,... ,n} then TL TL sin-(2Ttj/n)- n/2 so long as J关[m/2, where Laj is the greatest integer that is smaller than or equal to x (c) Show that when j 0 we have...
Solve and show work for problem 8 Problem 8. Consider the sequence defined by ao = 1, ai-3, and a',--2an-i-an-2 for n Use the generating function for this sequence to find an explicit (closed) formula for a 2. Problem 1. Let n 2 k. Prove that there are ktS(n, k) surjective functions (n]lk Problem 2. Let n 2 3. Find and prove an explicit formula for the Stirling numbers of the second kind S(n, n-2). Problem 3. Let n 2...
. Prove that sequence in Example 6.2.2 (i) on p.174 converges uniformly to r on any inteval [a, b]. Prove that the convergence cannot be uniform on [0, 0o) J() d tel argue thau Jn J Exercise 6.2.6. Assume fn → f on a set A. Theorem 6.2.6 is an example of a typical type of question which asks whether a trait possessed by each fn is inherited by the limit function. Provide an example to show that all of...
7) The value to (n-1) of nl (n) is equal True or falle false J 30 TL 3 The sequence geometric 5, 1, -3, -2, i sequence Truce as False