If the random variable X is exponentially distributed with parameter = 1.5,then P(2 X 4),up to 4 decimal places,is
A)0.6667
B)0.0473
C)0.5000
D)0.2500

Question

If the random variable X is exponentially distributed with parameter  = 1.5,then P(2  X  4),up to 4 decimal places,is
A)0.6667 
B)0.0473 
C)0.5000 
D)0.2500

Quizplus · Accepted Answer

Since X is exponentially distributed with parameter λ = 1.5, the probability density function (PDF) of X is given by:

f(x) = λe^(-λx) = 1.5e^(-1.5x)

To find P(2 < X < 4), we need to integrate f(x) over the interval [2, 4]:

P(2 < X < 4) = ∫[2,4] f(x) dx
             = ∫[2,4] 1.5e^(-1.5x) dx
             = [-e^(-1.5x)]_[2,4]
             = e^(-3) - e^(-1)
             ≈ 0.0473 (rounded to 4 decimal places)

Therefore, the best choice is B.

If the Random Variable X Is Exponentially Distributed with Parameter