If the random variable X is exponentially distributed with parameter $$\lambda$$ = 4, then the probability P(X $$\leq$$ 0.25), up to 4 decimal places, is:
A) $ 0.6321 $.
B) $ 0.3679 $.
C) $ 0.2500 $.
D) None of these choices are correct.

Question

If the random variable X is exponentially distributed with parameter $$\lambda$$ = 4, then the probability P(X $$\leq$$ 0.25), up to 4 decimal places, is: 
A) $ 0.6321 $.
B) $ 0.3679 $.
C) $ 0.2500 $.
D) None of these choices are correct.

Quizplus · Accepted Answer

The cumulative distribution function (CDF) for an exponential distribution is given by:
F(x) = 1 - e^(-λx)
We are given that λ = 4, so the CDF is:
F(x) = 1 - e^(-4x)
To find P(X ≤ 0.25), we substitute 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)
Therefore, the answer is choice A.

If the Random Variable X Is Exponentially Distributed with Parameter λ\lambdaλ

If the Random Variable X Is Exponentially Distributed with Parameter $\lambda$