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Probability space corresponding to this random experiment

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Reference no: EM132474387

Consider the following random experiment: we toss a fair coin repeatedly until the first "heads" occurs. The outcome ω is the number of coin flips in this sequence before (i.e. not including) the first heads.

Please solve

(a) Describe the probability space corresponding to this random experiment, detailing each component. Make sure to define what probability is assigned to any set in the σ-algebra.

(b) Consider the random variable X(ω) returning the value 1 if ω < 5 and 0 otherwise. Find the support of X. Is X discrete, continuous, or neither (mixed)? Justify.

(c) Compute P(X ∈ (2, 3]).

Reference no: EM132474387

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