Final answer:
The task involves finding probability values using an exponential distribution function, where the probabilities are calculated by using the complement of the cumulative distribution function (1 - CDF) for the exponential distribution.
Step-by-step explanation:
The question pertains to determining probabilities for a given exponential distribution function, which is represented as f(x) = e^(-x) for x > 0. In probability theory and statistics, the exponential distribution is used to model the time between events in a Poisson process. It's characterized by a constant average rate of occurrences and is therefore used to model the time or space between events that are independent and occur at a constant average rate.
For example, to find P(x > 20) for an exponential distribution, we would use the cumulative distribution function (CDF) to find P(X < x) and then subtract this from 1 to find P(X > x). The formula for the CDF of an exponential distribution is P(X < x) = 1 - e-mx, where 'm' is the rate parameter. Hence, to calculate P(x > 20), we need the correct value for 'm' in the context of X~Exp(m), which might be given elsewhere in the question. If 'm' was 0.5, for instance, then P(x > 20) would be 1 minus the CDF at x = 20, which is 1 - e-0.5 * 20 = e-10.