Question

The lifetime X of an alkaline battery is exponentially distributed with lambda = 0.05 per hour. What are the mean and standard deviation of the battery’s lifetime

Answer 1

If a random variable $X$ is exponentially distributed with rate $λ,$ then

$$E(X)=\dfrac{1}{\lambda}, Var(X)=\sigma^2=(\dfrac{1}{\lambda})^2$$

Given $\lambda=0.05.$ Then

$$E(X)=\dfrac{1}{0.05}=20, \sigma=\sqrt{\sigma^2}=\dfrac{1}{0.05}=20$$