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Discrete Mathematics

# 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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