Math Problem Statement
Let X = the time between two successive arrivals at the drive-up window of a local bank. If X has an exponential distribution with l = 1, compute the following:
a. The expected time between two successive arrivals
b. The standard deviation of the time between successive arrivals
c. P(X ≤ 4)
d. P(2 ≤ X ≤ 5)
Solution
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Math Problem Analysis
Mathematical Concepts
Probability
Exponential Distribution
Expected Value
Standard Deviation
Cumulative Distribution Function (CDF)
Formulas
Expected Value: E(X) = 1/λ
Standard Deviation: σ(X) = 1/λ
CDF of Exponential Distribution: F(x) = 1 - e^(-λx)
P(X ≤ x): F(x) = 1 - e^(-λx)
Theorems
Properties of Exponential Distribution
Suitable Grade Level
Grades 11-12
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