1. Let (X) be a simple random walk that starts from Xo = 0 and on each step goes up one with%3Dprobability p and down one with probability q = 1 – p.Calculate:(a) P(X, = 0),(b) EX.,(c) Var(X6),(d) E(X10 | X4 = 4).(e) P(X19 = 0 | Xg = 2),(f) P(X, = 2| X 10 = 6).Consider the case p = 0.6, so q = 0.4.(g) What are EX100and Var(X100)?(h) Using a normal approximation, estimate P(16 S X100 S 26). You should use an appropriate"continuity correction", and explain why you chose it. (Bear in mind the possible values X00 cantake.)

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Answered: 1. Let (X) be a simple random walk that…

1. Let (X) be a simple random walk that starts from X, = 0 and on each step goes up one with probability p and down one with probability q = 1 – p. %3D Calculate: (a) P(X, = 0), (b) EX (c) Var(X6),

Trigonometry (MindTap Course List)

10th Edition

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Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.4: Hyperbolas

Problem 5ECP: Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.

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Question

1. Let (X) be a simple random walk that starts from Xo = 0 and on each step goes up one with
%3D
probability p and down one with probability q = 1 – p.
Calculate:
(a) P(X, = 0),
(b) EX.,
(c) Var(X6),
(d) E(X10 | X4 = 4).
(e) P(X19 = 0 | Xg = 2),
(f) P(X, = 2| X 10 = 6).
Consider the case p = 0.6, so q = 0.4.
(g) What are EX100
and Var(X100)?
(h) Using a normal approximation, estimate P(16 S X100 S 26). You should use an appropriate
"continuity correction", and explain why you chose it. (Bear in mind the possible values X00 can
take.)

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