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

We know that X follows an exponential distribution with parameter $\lambda=1.5$. The probability density function (pdf) of X can be given by:

$f(x) = \lambda e^{-\lambda x}$, for $x \geq 0$

We need to find P(2<X<4).

Using the cumulative distribution function (cdf) of X, we can write:

$P(2<X<4) = \int_{2}^{4} f(x) dx = \int_{2}^{4} 1.5e^{-1.5x} dx$

Solving the integral, we get:

$P(2<X<4) = e^{-3} - e^{-1} \approx 0.0473$

Therefore, the best answer choice is B.

If the Random Variable X Is Exponentially Distributed with Parameter