If the random variable X is exponentially distributed with parameter $\lambda$ = 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

For an exponential distribution, the probability of X being in an interval depends on the length of the interval and the rate parameter λ. Since the intervals (1,2) and (2,3) have the same length and λ is constant, the probabilities are equal. However, the statement is false because the intervals are not equal in terms of probability due to the nature of the exponential distribution's decreasing probability density function.

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

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