Probability

Continuous Probability Distributions

Continuous Probability Distributions - Uniform Distribution

         

XX is a random variable that follows a continuous uniform distribution with probability density function f(x)={112(5x17)0(elsewhere).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 xx is a uniformly distributed random variable that has probability density function f(x)f(x) in the interval [6,17],[6,17], what is cc in the above diagram?

xx is a random variable that follows a uniform distribution with the following probability density function: f(x)={114(axb)0(elsewhere).f(x) = \left\{\begin{matrix} \frac{1}{14} & (a \leq x \leq b) \\ 0 & (\text{elsewhere}). \end{matrix}\right. If the value of a+ba+b is 20,20, what is the value of a×b? a \times b?

XX is a random variable that has a continuous uniform distribution with the probability density function f(x)={126(5x31)0(elsewhere).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?

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

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