[8] 3. In a process of sintering(heating) two types of copper powder, the density function for Y1, the volume proportion of solid copper in a sample, was given by J 6y1(1 – y1) 0< y1 < 1 f1(y1) = elsewhere The density function for Y2, the proportion of type A crystals among the solid copper, was given as (3y 0< y2 <1 f2(४2) = elsewhere The variable U = YY2 gives the proportion of the sample volume due to type A crystals. If Yi and Y, are independent, find the probability density function for U.

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