Question: A register contains eight random binary digits which are mutually independent. Each digit is a zero or a one with equal probability. (A) Describe

A register contains eight random binary digits which are mutually independent. Each

A register contains eight random binary digits which are mutually independent. Each digit is a zero or a one with equal probability. (A) Describe an appropriate probability space (2, F, P) corresponding to looking at the contents of the register. (b) Express each of the following events explicitly as subsets of 2, and find their probabil- ities: El: "No two neighboring digits are the same," E2: "The register contains exactly four zeros," E3: "There is a run of at least six consecutive ones." (c) Find P(E1 | E2).

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