Question

An example of a uniform distribution is f(x) 1 for 0 x 1. The mean of the distribution for this example is 0.5 and the standard deviation is approximately 0.29. The graph of the distribution for this example is a square with the height and width both equal to 1 unit. In general, the density function for a uniform distribution on the interval from x a and x b is given by f(x).

(a) Find the probability that x falls between 0.25 and 0.5.
The probability is . (Type an integer or a decimal.)

Answer 1

A uniform distribution is a continuous probability distribution for a random variable between two values a and b(a<b), and where and all of the values of x are equally likely to occur. The graph of uniform distribution is shown below. (FIGURE CAN'T COPY) The probability density function of a uniform distribution is

on the interval from to For any value of less than a or greater than $b, y=0 .Use this information. Show that the probability density function of a uniform distribution satisfies the two conditions for a probability density function.

Explanation: