Uniform Distribution

The uniform distribution is a continuous probability distribution associated with events that are equally likely to occur.

Its probability density is expressed by a rectangular function where 'a' and 'b' are the lower and upper cut-offs, respectively.

For example, the voltage provided by the electricity company is uniformly distributed, say, between 122 and 126 volts.

In this case, the probability density is plotted as a function of the voltage supplied.

The total area under the graph should always be one. Since the range is 4 volts, the height must be one divided by 4.

One might wonder what is the probability of any household getting a voltage less than 123 volts?

It can be found from the area under the segment, which is the product of the width and height of the section.

This mean voltage supplied is the sum of the cut-off values divided by two, which in this case is a 124 volts.

The standard deviation is given by the range divided by the square root of twelve, which is found to be 1.2 volts.