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 S6y1 (1 – y1) 0< yı <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(y2) = elsewhere The variable U = YY, 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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[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
1o
f2(४2) =
elsewhere
The variable U = Y¡Y2 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.
Transcribed Image Text:[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 1o f2(४2) = elsewhere The variable U = Y¡Y2 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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