↑ Return to Random Variables

Exponential

\[\]

Exponential Distribution has the following properties:

  1. Equals the distance between successive occurances or arrivals of a Poisson process with mean $\lambda > 0$
  2. $\lambda$ is the average number of occurances or arrivals per unit of time (length, space, etc.)
  3. $\frac{1}{\lambda}$ is the average time between occurrences or arrivals.

\defl{Exponential Distribution:}

\[f(x) = \lambda e^{-{\lambda}x} \]


\[F(x) = 1- e^{-{\lambda}x} \]

  • $0 \leq x < \infty$
  • $\mu = E(X) =\frac{1}{\lambda}$
  • $\sigma^2 = V(X) = \frac{1}{\lambda^2}$
\defs{Examples}
  • The amount of time until the next customer at The Pizza Customer will arrive.
  • The amount of time until the DVD player will break. The exponential distribution is very useful for determining length of warranty.
  • The amount of time until the next person will arrive at a specific ATM