killobingo.blogg.se

The probability density function is given by: Typical questions may be, “what is the probability that some event will occur within the next hours or days, or what is the probability that some event will occur between hours and hours, or what is the probability that the event will take more than hours to perform?” In short, the random variable X equals ( a) the time between events or ( b) the passage of time to complete an action, e.g. The random variable for the exponential distribution is continuous and often measures a passage of time, although it can be used in other applications. There are more people who spend small amounts of money and fewer people who spend large amounts of money.Įxponential distributions are commonly used in calculations of product reliability, or the length of time a product lasts. For example, marketing studies have shown that the amount of money customers spend in one trip to the supermarket follows an exponential distribution. There are fewer large values and more small values. Values for an exponential random variable occur in the following way. It can be shown, too, that the value of the change that you have in your pocket or purse approximately follows an exponential distribution.

Other examples include the length of time, in minutes, of long distance business telephone calls, and the amount of time, in months, a car battery lasts. For example, the amount of time (beginning now) until an earthquake occurs has an exponential distribution. The exponential distribution is often concerned with the amount of time until some specific event occurs. Continuous Random Variables 28 The Exponential Distribution