Asked by Anthony Ventura on Sep 28, 2024
Verified
If the random variable X is exponentially distributed with parameter λ = 0.05,then the probability P(X > 20)= 0.3679.
Exponentially Distributed
A statistical term used to describe the time between events in a Poisson point process, where events occur continuously and independently at a constant average rate.
Random Variable
An element with numerical values produced by the uncertainty of events.
- Ascertain the probabilistic values attributed to exponential distributions.
Verified Answer
FD
Fernanda De liraabout 2 hours ago
Final Answer :
True
Explanation :
Using the cumulative distribution function of the exponential distribution, we have:
P(X > 20) = 1 - P(X ≤ 20)
= 1 - (1 - e^(-λx)) (where x=20 and λ=0.05)
= 1 - (1 - e^(-1))
= e^(-1)
= 0.3679
Therefore, the statement is true and the answer is option A.
P(X > 20) = 1 - P(X ≤ 20)
= 1 - (1 - e^(-λx)) (where x=20 and λ=0.05)
= 1 - (1 - e^(-1))
= e^(-1)
= 0.3679
Therefore, the statement is true and the answer is option A.
Learning Objectives
- Ascertain the probabilistic values attributed to exponential distributions.
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