Mean and Variance of an Exponential

Integrate $x$ against the exponential density to find the mean.

The exponential distribution's variance equals the square of its mean.

1. 1. State the mean

   For $X\sim \text{Exponential}(\lambda )$, $E[X]=\frac{1}{\lambda }$.

2. 2. State the variance

   The variance of the exponential distribution is the square of its mean.

   $$\text{Var}(X)=\frac{1}{{\lambda }^2}$$

Answer: Mean = 1/lambda, variance = 1/lambda^2