If the random variable X is exponentially distributed with parameter λ = 4,then the probability P(X ≤ 0.25)is equal to:
A)0.6321
B)0.3679
C)0.2500
D)0.5000

Question

Quizplus · Accepted Answer

The cumulative distribution function (CDF) for an exponential distribution with parameter λ is given by F(x) = 1 - e^(-λx). 
Thus, for λ = 4, we have F(x) = 1 - e^(-4x). 
To find P(X ≤ 0.25), we simply evaluate F(0.25): 
P(X ≤ 0.25) = F(0.25) = 1 - e^(-4*0.25) = 1 - e^(-1) = 0.6321.

Therefore, the answer is choice A.

If the Random Variable X Is Exponentially Distributed with Parameter