What is the mean of x, given the exponential probability function $$f ( x ) = \frac { 1 } { 20 } e ^ { \frac { x } { 20 } } \text { for } x \geq 0 \text { ? }$$
A)0.05
B)20
C)100
D)2,000

Question

Quizplus · Accepted Answer

The mean ($\mu$) of an exponential distribution is given by $\mu = \frac{1}{\lambda}$, where $\lambda$ is the rate parameter of the distribution. In the given function $f(x) = \frac{1}{20}e^{\frac{x}{20}}$, $\lambda = \frac{1}{20}$. Therefore, the mean is $\mu = \frac{1}{\lambda} = \frac{1}{\frac{1}{20}} = 20$.

What Is the Mean of X, Given the Exponential Probability f(x)=120ex20 for x≥0 ? f ( x ) = \frac { 1 } { 20 } e ^ { \frac { x } { 20 } } \text { for } x \geq 0 \text { ? }f(x)=201​e20x​ for x≥0 ?

What Is the Mean of X, Given the Exponential Probability $f ( x ) = \frac { 1 } { 20 } e ^ { \frac { x } { 20 } } \text { for } x \geq 0 \text { ? }$