2.6. Let (2, F, P) be a probability space and let A1, A2,... be sets in Fsuch thatP(Ag) < ∞ .k=1Prove the Borel-Cantelli lemma:P(N U Ak) = 0,m=1 k=mi.e. the probability that w belongs to infinitely many A{s is zero.

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Answered: 6. Let (N,F, P) be a probability space…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Let’s suppose that U is a random variable which is uniformly distributed on the interval [0, 1]. Compute each of the following.
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Background: A dog named Zip is often tied to a zipline. Fig 1A: Top view of yard. When tied, Zip travels in such a way that the hook on the line slides back and forth as he moves. A coordinate system is defined as described in the picture to the right. Figure 1A shows a top view and Figure 1B shows a Fig 1B: Sideview of zipline. sideview. A measurement system is connected to the hook. It periodically records the position on the line during the time Zip is connected to it. After 50,000 x=0 location of hook observations (electronically recorded) a continuous model for where the hook is located was developed by - 10m < x < 10m a team of engineers. They came up with the model that p(x) = {A + 10) otherwise 1) Sketch a graph for p(x). Do you need to fill in this form? You can use Fill & Sign to complete form yourself or get others to sign. 2) What is the average position of the hook on the zipline?
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6. Let (N,F, P) be a probability space and let A1, A2,. be sets in F such that P(Aµ) < ∞. Prove the Borel-Cantelli lemma: P(N U Ak) = 0, m=1 k=m i.e. the probability that w belongs to infinitely many As is zero.