Final answer:
The CDF of an exponential distribution is P(X ≤ x) = 1 - e-mx, where 'm' is the decay parameter. It provides the cumulative probability that a random variable X is less than or equal to x.
Step-by-step explanation:
The Cumulative Distribution Function (CDF) of an exponential distribution for a random variable X, notated as X~Exp(m), is the function that gives the probability that X is less than or equal to a certain value x. For the exponential distribution, the CDF is defined mathematically as:
P(X ≤ x) = 1 - e-mx
where 'm' is the decay parameter, x is the value for which we want to find the cumulative probability, and e is the base of the natural logarithm. For an exponential distribution with a decay parameter of 0.5, the CDF would be:
P(X < x) = 1 - e-(0.5)x
Using the CDF, we can also calculate the complementary probability, which is P(X > x), by subtracting the CDF from 1:
P(X > x) = 1 - P(X ≤ x)
The exponential distribution is also characterized by the memoryless property, meaning that the remaining waiting time until an event occurs is independent of how much time has already passed.