Consider a probability model for which the sample space (i.e., the set of possible outcomes ω) is the nonnegative real axis: Ω = [0,∞). For any positive integer n, let An be the event {ω ∈ Ω : ω ≥ n}, i.e., the interval [n, ∞). Give a rigorous proof (justifying steps using the axioms of probability, whenever appropriate) that limn→∞ P(An) = 0.

Consider a probability model for which the sample space (i.e., the set of possible outcomes ω) is the nonnegative real axis: Ω = [0,∞). For any positive integer n, let An be the event {ω ∈ Ω : ω ≥ n}, i.e., the interval [n, ∞). Give a rigorous proof (justifying steps using the axioms of probability, whenever appropriate) that limn→∞ P(An) = 0.

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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Definition Definition For any random event or experiment, the set that is formed with all the possible outcomes is called a sample space. When any random event takes place that has multiple outcomes, the possible outcomes are grouped together in a set. The sample space can be anything, from a set of vectors to real numbers.

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