APPLY YOUR KNOWLEDGE 3.2 A uniform distribution. Figure 3.6 displays the density

Question

APPLY YOUR KNOWLEDGE 3.2 A uniform distribution. Figure 3.6 displays the density curve of a uniform distribution. The curve takes the constant value I over the interval from 0 to 1 and is zero outside that range of values. This means that data described by this distribution take values that are uniformly spread between 0 and 1. Use areas under this density curve to answer the following questions. (a) Why is the total area under this curve equal to 1 (b) What percent of the observations lie above 0.8 (c) What percent of the observations lie below 0.6? (d) What percent of the observations lie between 0.25 and 0.752 height-1 FIGURE 3.6 The density curve of a uniform distribution, for Exercises 3.2 and 3.3

Explanation / Answer

a. Area is width * height

here width =1 and height = 1

Area = 1

b. % of observations above are

total - observations under 0.8 = 1-(0.8*1) = 0.2 = 20%

c.   

% of observations below 0.6 are

= (0.6*1) = 0.6 = 60%

d.

% of observation between 0.75 and 0.25

% below 0.75 - % below 0.25

=0.75-0.25 = 0.5 = 50%

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