Uniform Distribution

Uniform Distribution

• The curve is a flat line on the interval $[a,b]$, where $a$ is the lowest possible value of $X$ and $b$ is the highest possible value of $X$
• The probability that the random variable takes on any value between $x_1$ and $x_2$ is the area of the rectangle under the curve, between $x_1$ and $x_2$
• $P(x_1<X<x_2)=(x_2-x_1)\times\frac{1}{b-a}$
• The mean of a uniform distribution is $\boxed{E(X)=\mu=\frac{a+b}{2}}$$$
• This is the "middle" value of the interval
• The standard deviation of the uniform distribution $\boxed{\displaystyle SD(X)=\sigma=\sqrt{\frac{(b-a)^2}{12}}}$