If the random variable X is exponentially distributed with parameter λ = 4,then the probability P(X ≤ 0.25),up to 4 decimal places,is
A)0.6321
B)0.3679
C)0.2500
D)None of these choices.

Question

Quizplus · Accepted Answer

The cumulative distribution function (CDF) of an exponentially distributed random variable with parameter λ is given by:
F(x) = 1 − e^(−λx)
Therefore, for λ = 4, we have F(x) = 1 − e^(−4x)
To find P(X ≤ 0.25), we plug in x = 0.25 into the CDF:
P(X ≤ 0.25) = F(0.25) = 1 − e^(−4×0.25) ≈ 0.6321 (rounded to 4 decimal places)

If the Random Variable X Is Exponentially Distributed with Parameter