Asked by Andrea Noriega on May 25, 2024
Verified
If the random variable X is exponentially distributed with parameter λ = 0.05,then the probability P(X < 5)= .2865.
Exponentially Distributed
Pertaining to a statistical distribution characterized by a constant rate of decay or growth over time.
Random Variable
A variable whose outcomes are determined by the occurrences of a random event.
- Calculate probabilities related to exponential distributions.
- Elucidate the parameter λ in exponential distributions and recognize its relationship to mean and variance.
Verified Answer
ZK
Zybrea KnightJun 01, 2024
Final Answer :
False
Explanation :
The probability that X < 5 for an exponential distribution with λ = 0.05 is calculated using the cumulative distribution function (CDF): P(X < 5) = 1 - e^(-λx) = 1 - e^(-0.05*5) = 1 - e^(-0.25) ≈ 0.2212, not 0.2865.
Learning Objectives
- Calculate probabilities related to exponential distributions.
- Elucidate the parameter λ in exponential distributions and recognize its relationship to mean and variance.
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