13. Let {Xn, n ≥ 1} be iid with P[X₁ = 1] = p = 1 - P[X₁ = 0]. What isthe probability that the pattern 1,0,1 appears infinitely often?Hint: LetAk = [Xk = 1, Xk+1=0, Xk+2 =1]and consider A₁, A4, A7, ....

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Answered: 13. Let {Xn, n ≥ 1} be iid with P[X₁ =…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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5.5-9 a only
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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13. Let {Xn, n ≥ 1} be iid with P[X₁ = 1] = p = 1 - P[X₁ = 0]. What is the probability that the pattern 1,0,1 appears infinitely often? Hint: Let A} = [X} = 1, Xk+=0, Xk+2=1] and consider A1, A4, A7, ....