Question

How to find standard deviation of continuous uniform distribution?

Answer 1

The uniform distribution is used to describe

a situation where all possible outcomes of

a random experiment are equally likely to

occur. You can use the variance and

standard deviation to measure the

“spread” among the possible values of the

probability distribution of a random

variable.

For example, suppose that an art gallery

sells two types of art work: inexpensive

prints and original paintings. The length of

time that the prints remain in inventory is

uniformly distributed over the interval (0,

40). For example, some prints are sold

immediately; no print remains in inventory

for more than 40 days. For the paintings,

the length of time in inventory is uniformly

distributed over the interval (5, 105). For

example, each painting requires at least 5

days to be sold and may take up to 105

days to be sold.

The variance and the standard deviation

measure the degree of dispersion (spread)

among the values of a probability

distribution. In the art gallery example, the

inventory times of the prints are much

closer to each other than for the paintings.

As a result, the variance and standard

deviation are much lower for the prints

because the range of possible values is

much smaller.