Exercise 11. Let P be a probability on (R, B(R)). P is called tight if for any e > 0, there is acompact set KCR such that P(Kº) < E.(a)For n N, show that [-n, n] is compact (under the metric d(y, z) = |yz| fory, z € R).(b)Show that P is tight.

is a probability on .There is a compact set such that .

Answered: Exercise 11. Let P be a probability on…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Exercise 11. Let P be a probability on (R, B(R)). P is called tight if for any e > 0, there is a compact set KCR such that P(K) < e. (a) For n N, show that [-n, n] is compact (under the metric d(y, z) = y - z for (b) y, z E R). Show that P is tight.