Let X be the amount of time (in hours) the wait is to get a table at a restaurant. Suppose the cdf is represented by Use the cdf to determine E[X]. F(x) 0 7³ 27 1 I <0 0≤x≤3 I > 3

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Let \( X \) be the amount of time (in hours) the wait is to get a table at a restaurant. Suppose the cumulative distribution function (cdf) is represented by

\[
F(x) = 
\begin{cases} 
0, & x < 0 \\
\frac{x^3}{27}, & 0 \leq x \leq 3 \\
1, & x > 3 
\end{cases}
\]

Use the cdf to determine \( E[X] \).
Transcribed Image Text:Let \( X \) be the amount of time (in hours) the wait is to get a table at a restaurant. Suppose the cumulative distribution function (cdf) is represented by \[ F(x) = \begin{cases} 0, & x < 0 \\ \frac{x^3}{27}, & 0 \leq x \leq 3 \\ 1, & x > 3 \end{cases} \] Use the cdf to determine \( E[X] \).
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