In the production of a certain type of copper, two types of copper powder (types A and

Chapter 5, Problem 5.152

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In the production of a certain type of copper, two types of copper powder (types A and B) are mixed together and sintered (heated) for a certain length of time. For a fixed volume of sintered copper, the producer measures the proportion Y1 of the volume due to solid copper (some pores will have to be filled with air) and the proportion Y2 of the solid mass due to type A crystals. Assume that appropriate probability densities for Y1 and Y2 are f1(y1) = 6y1(1 y1), 0 y1 1, 0, elsewhere, f2(y2) = 3y2 2 , 0 y2 1, 0, elsewhere. The proportion of the sample volume due to type A crystals is then Y1Y2. Assuming that Y1 and Y2 are independent, find P(Y1Y2 .5).

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