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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.)

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Answer:

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.

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