- conditional probability
- the likelihood that an event will occur given that another event has already occurred
- decay parameter
- the description of the rate at which probabilities decay to zero for increasing values of x
It is the value m in the probability density function f(x) = me(–mx) of an exponential random variable. It is also equal to m = , where μ is the mean of the random variable.
- exponential distribution
- a continuous random variable (RV) that appears when we are interested in the intervals of time between some random events, for example, the length of time between emergency arrivals at a hospital; the notation is X ~ Exp(m)
The mean is μ = and the standard deviation is σ = . The probability density function is f(x) = me−mx, x ≥ 0, and the cumulative distribution function is P(X ≤ x) = 1 − e−mx.
- memoryless property
- or an exponential random variable X, the statement that knowledge of what has occurred in the past has no effect on future probabilities
This means that the probability that X exceeds x + k, given that it has exceeded x, is the same as the probability that X would exceed k if we had no knowledge about it. In symbols we say that P(X > x + k|X > x) = P(X > k).
- Poisson distribution
- a distribution function that gives the probability of a number of events occurring in a fixed interval of time or space if these events happen
with a known average rate and independently of the time since the last event; if there is a known average of λ events occurring per unit time, and these events are independent of each other, then the number of events X occurring in one unit of time has the Poisson distribution
- uniform distribution
- a continuous random variable (RV) that has equally likely outcomes over the domain, a < x < b. Notation—X ~ U(a,b)
The mean is μ = and the standard deviation is . The probability density function is f(x) = for a < x < b or a ≤ x ≤ b. The cumulative distribution is P(X ≤ x) = .