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Discrete Mathematics

Continuous Probability Distributions

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?

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?

\(x\) 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 \( a \times b?\)

\(X\) 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?

\(x\) 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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