Continuous Probability Distributions - Uniform Distribution

\(X\) is a random variable that follows a continuous uniform distribution with probability density function
\[f(x) = \left\{\begin{matrix}
\frac{1}{12} & (5 \leq x \leq 17) \\
0 & (\text{elsewhere}).
\end{matrix}\right. \]
Then what is the mean of the distribution?

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If \(x\) is a uniformly distributed random variable that has probability density function \(f(x)\) in the interval \([6,17],\) what is \(c\) in the above diagram?

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\(x\) is a random variable that follows a uniform distribution with the following probability density function:
\[f(x) = \left\{\begin{matrix}
\frac{1}{14} & (a \leq x \leq b) \\
0 & (\text{elsewhere}).
\end{matrix}\right. \]
If the value of \(a+b\) is \(20,\) what is the value of \( a \times b?\)

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\(X\) is a random variable that has a continuous uniform distribution with the probability density function
\[f(x) = \left\{\begin{matrix}
\frac{1}{26} & (5 \leq x \leq 31) \\
0 & (\text{elsewhere}).
\end{matrix}\right. \]
Then what is the variance of the distribution?

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\(x\) is a random variable that has a uniform distribution in the interval \([1,7].\) What is the probability of the random variable \(x\) taking on values greater than \(4?\)

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