If the random variable X is exponentially distributed with parameter λ = 2,then the probability that X is between 1 and 2 equals the probability that X is between 2 and 3.

Question

Quizplus · Accepted Answer

The probability that a continuous random variable falls within a particular interval is equal to the integral of the probability density function over that interval. The probability density function for an exponential distribution with parameter λ is f(x) = λe^(-λx), therefore the probability that X is between 1 and 2 is:
∫(from 1 to 2)λe^(-λx)dx = e^(-2) - e^(-4) ≈ 0.218
The probability that X is between 2 and 3 is:
∫(from 2 to 3)λe^(-λx)dx = e^(-4) - e^(-6) ≈ 0.0498
These probabilities are not equal, so the statement is false.

If the Random Variable X Is Exponentially Distributed with Parameter