This applet computes probabilities and percentiles for the exponential distribution:
$$X \sim exp(\lambda)$$
When using scale parameterization, replace $\lambda$ with $\frac{1}{\beta}$ in the following equations.
Directions
- Enter the rate in the $\lambda$ box.
- To compute a left-tail probability, select $P(X \lt x)$ from the drop-down box,
enter a numeric $x$ value in the blue
box and press "Tab" or "Enter" on your keyboard. The probability
$P(X \lt x)$ will appear in the pink box.
Select $P(X \gt x)$ from the drop-down box for a right-tail probability.
- To determine a percentile, enter the percentile (e.g. use 0.8 for the 80th percentile) in the
pink
box, select $P(X \lt x)$ from the drop-down box, and press "Tab" or "Enter" on your keyboard. The percentile $x$ will appear in the blue box.
On the graph, the $x$ value appears in
blue
while the probability is shaded in
pink.
Details
- Probability density function
$$f(x)=\lambda e^{-\lambda x}\quad$$
where $x>0$ and $\lambda > 0$.
- $\mu=E(X)=\frac{1}{\lambda}$
- $\sigma^2=Var(X)=\frac{1}{\lambda^2}$
- $\sigma=SD(X)=\frac{1}{\lambda}$