Describe the sigma-field F2. (Write down All elements of F2). Hint: How many outcom if we toss a coin two times? Then how many subsets for the set including all of t outcomes?

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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(b) Describe the sigma-field F2. (Write down All elements of F2). Hint: How many outcomes
if we toss a coin two times? Then how many subsets for the set including all of the
outcomes?
Given {N(t)} is a Poisson process, please calculate
(a) P(N(4)=2|N(2)=1)
(b) E[N(4)|N(2)=1]
(c) Var[N(4)|N(2)=1]
(d) P(N(4)=2|N(10)=5), also calculate E[N(4)|N(10)=5] and Var[N(4)|N(10)=5]
Transcribed Image Text:(b) Describe the sigma-field F2. (Write down All elements of F2). Hint: How many outcomes if we toss a coin two times? Then how many subsets for the set including all of the outcomes? Given {N(t)} is a Poisson process, please calculate (a) P(N(4)=2|N(2)=1) (b) E[N(4)|N(2)=1] (c) Var[N(4)|N(2)=1] (d) P(N(4)=2|N(10)=5), also calculate E[N(4)|N(10)=5] and Var[N(4)|N(10)=5]
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