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5. Let 2 = {w1, w2,w3, wa, w5, W6}. Consider the filtration F = (Fi)i=0,1,2.3 given as follows: F, = {N, Ø}, F = 0(A1, A2), where A - {wi,w2, ws}, A2 - {w3,wa, ws}, {w's, wa, wg}, F2 = 0(B1, B2, B3), where B = {w1, w2}, B, = {w3,ws}, B3 = {w4, ws}; %3D and F3 = P()-the power set of 2. Let P(wi) = 0.1, P(w2) = 0.1, P(w3) = 0.4, P(w4) = 0.2, P(w5) = 0.1, P(w6) = 0.1. %3D Let X (wi) = -2, X (w2) = 1, X(w3) = 4, X(wA) = 0, X(ws) = -1, X(w6) = 7. Find the stochastic process (X;);=0,1,2,3 , where X; = E(X | F;).

5. Let 2 = {w1, w2,w3, wa, w5, W6}. Consider the filtration F = (Fi)i=0,1,2.3 given as follows: F, = {N, Ø}, F = 0(A1, A2), where A - {wi,w2, ws}, A2 - {w3,wa, ws}, {w's, wa, wg}, F2 = 0(B1, B2, B3), where B = {w1, w2}, B, = {w3,ws}, B3 = {w4, ws}; %3D and F3 = P()-the power set of 2. Let P(wi) = 0.1, P(w2) = 0.1, P(w3) = 0.4, P(w4) = 0.2, P(w5) = 0.1, P(w6) = 0.1. %3D Let X (wi) = -2, X (w2) = 1, X(w3) = 4, X(wA) = 0, X(ws) = -1, X(w6) = 7. Find the stochastic process (X;);=0,1,2,3 , where X; = E(X | F;).

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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5. Let 2 = {wi, w2, w3, w4,ws, w6}. Consider the filtration F = (Fi)i=0,1.2.3 given as follows: Fo = {N, Ø}, F1 = 0(A1, A2), where A - {wi, w2, wis}; A2 F2 = 0(B1, B2, B3), where B = {w1, w2}, B2 = {w3,ws}, B3 = {w4, wo}; and F3 = P()-the power set of . Let P(w1) = 0.1, P(w2) = 0.1, P(w3) = 0.4, P(w4) = 0.2, P(w5) = 0.1, P(w6) = 0.1. Let X (wi) = -2, X(w2) = 1, X (w3) = 4, X(w4) = 0, X(ws) = -1, X(w6) = 7. Find the stochastic process (X;);=0,1,2,3 , where X; = E(X | F;).
Transcribed Image Text:5. Let 2 = {wi, w2, w3, w4,ws, w6}. Consider the filtration F = (Fi)i=0,1.2.3 given as follows: Fo = {N, Ø}, F1 = 0(A1, A2), where A - {wi, w2, wis}; A2 F2 = 0(B1, B2, B3), where B = {w1, w2}, B2 = {w3,ws}, B3 = {w4, wo}; and F3 = P()-the power set of . Let P(w1) = 0.1, P(w2) = 0.1, P(w3) = 0.4, P(w4) = 0.2, P(w5) = 0.1, P(w6) = 0.1. Let X (wi) = -2, X(w2) = 1, X (w3) = 4, X(w4) = 0, X(ws) = -1, X(w6) = 7. Find the stochastic process (X;);=0,1,2,3 , where X; = E(X | F;).
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