### Exponential Distribution$X \sim exp(\lambda)$

 Rate Scale   $\lambda=$ $x=$ P(X > x) = P(X < x) =

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 $\lambda > 0$.
• $\mu=E(X)=\frac{1}{\lambda}$
• $\sigma^2=Var(X)=\frac{1}{\lambda^2}$
• $\sigma=SD(X)=\frac{1}{\lambda}$