Question

A distribution is given as

X ~ U(0, 12).



What is the probability density function? (Enter exact numbers as integers, fractions, or decimals.)

f(x) = ? , where ? ≤ x ≤ ?

Answer 1

If X is uniformly distributed on the interval (0, 12), then its PDF is

`f_X(x) = \begin{cases}\frac1{12} & \text{if }0 < x < 12 \\ 0&\text{otherwise}\end{cases}`

or simply

`f_X(x) = \frac1{12} \text{ where } 0 < x < 12`

and the zero-elsewhere case is assumed.

Whether you include 0 and 12 in the domain is irrelevant, since the probability that X = 0 or X = 12 are both zero.