, , etc., are 13%, 5%, etc., illustrating that there is always a finite number of "surviving" atoms remaining in their original state and awaiting decay, but their number decreases exponentially over time. Other applications of the exponential PDF can be found in daily life. For instance, if a person regularly drives above the speed limit and if the highway patrol makes regular controls, the probability of getting a speeding ticket only after a given time t, i.e., p(T > t) = exp(-t/t), is rapidly vanishing, just like the drivers' luck. The probability that he or she will get a ticket before time t, i.e., p(T < t) = 1 - exp(-t/t), is rapidly 2.4 Uniform, exponential, and Gaussian distributions increasing towards unity, representing a situation reaching 100% likelihood. If T = 1 year represents the mean time for bad drivers to get a speeding ticket, the probability of only getting a ticket 2 to 3 years after that time is only 13% to 5%, meaning that there is an 87% to 95% chance of getting it well before then! The exponential distribution is also used to characterize reliability and failure in manufactured products or systems, such as TV sets or car engines. Given the mean time to observe a given failure, T (now called mean time to failure or MTTF), the probabilities that the failure will be observed before or after time t are p(T<t) = 1 - exp(-t/t) or p(T>t) = exp(-t/t), respectively. The function p(T>t) is generally referred to as the reliability function. Its complement, p(T <<) = 1 - p(T>t) is referred to as the failure function. For instance, if T = 5 years represents the mean time to get a car-engine problem, the probability of getting the problem within one year is p(T<1 year) = 1 - exp(-1/5) = 0.18, and after one year p(T>1 year) = 1 - p(T < 1 year) = 0.82. This means that there is close to a 20% chance of having the problem before one year, even if the car engine (or driving safety) is supposed to be problem-free for a mean period of 5 years. On the other hand, the odds of having a problem after one year a