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Continuous Probability Distributions

How much variation should you have in your blood pressure? How likely is that stock price to double by the end of the year? Use continuous probability distributions to find out!

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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