If the random variable X is exponentially distributed with parameter λ = 0.05,then the probability P(X 20)= 0.3679.

Question

If the random variable X is exponentially distributed with parameter λ = 0.05,then the probability P(X > 20)= 0.3679.

Quizplus · Accepted Answer

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.

If the Random Variable X Is Exponentially Distributed with Parameter