6.84 In blending fine and coarse powders prior to copper sintering, proper blending is necessary for uniformity in the finished product. One way to check the blending is to select many small random samples of the blended powders and measure the weight fractions of the fine particles.

These measurements should be relatively constant if good blending has been achieved.

a Suppose the weight fractions have a beta distribution with 3. Find their mean and variance.

b Repeat part

(a) for 2.

c Repeat part

(a) for 1.

d Which of the three cases, (a), (b), or (c), would exemplify the best blending?