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The given exponential probability density function (PDF) is:

\[
f(x) = \frac{1}{20} e^{-\frac{x}{20}}
\]

This is the form of an exponential distribution, where the PDF is generally given by:

\[
f(x) = \frac{1}{\theta} e^{-\frac{x}{\theta}}
\]

In this case, \(\theta = 20\). The parameter \(\theta\) is the mean (or expected value) of the exponential distribution.

Thus, the mean of \(x\) is:

\[
\mu = \theta = 20
\]

Therefore, the correct answer is:

**b. 20**

Would you like more details or have any questions? 

Here are 5 related questions to explore further:
1. What is the variance of an exponential distribution with parameter \(\theta\)?
2. How is the median of an exponential distribution calculated?
3. How can the exponential distribution be used to model waiting times?
4. What is the cumulative distribution function (CDF) for this exponential distribution?
5. How would the PDF change if the mean were 50 instead of 20?

**Tip:** In an exponential distribution, the parameter \(\theta\) represents both the mean and the standard deviation.

What is the mean of x, given the exponential probability function (1/20)e^(-x/20)?

Learn how to calculate the mean of x given an exponential probability function (1/20)e^(-x/20). Understand key concepts such as the exponential distribution, and explore related questions like the variance and median of the distribution.

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