Math Problem Statement
Solution
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Math Problem Analysis
Mathematical Concepts
Geometric Distribution
Expected Value
Infinite Geometric Series
Formulas
Probability Mass Function of Geometric Distribution: P(X = k) = (1 - p)^{k-1}p
Expected Value of a Geometric Series: E(1/2^X) = Σ(1/2^k * P(X = k))
Sum of Infinite Geometric Series: S = a / (1 - r)
Theorems
Geometric Series Sum Theorem
Suitable Grade Level
Undergraduate (Probability and Statistics)
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