Math Problem Statement

Give final answer for each part

Solution

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Math Problem Analysis

Mathematical Concepts

Exponential Distribution
Probability
Conditional Probability

Formulas

Standard Deviation (SD(X)) = 1 / lambda
CDF of Exponential Distribution: F(x; lambda) = 1 - e^(-lambda * x)
Conditional Probability for Exponential Distribution: P(X ≤ a | X > b) = (F(a) - F(b)) / (1 - F(b))

Theorems

Exponential Distribution Properties
Conditional Probability

Suitable Grade Level

College-level Statistics