In a process of sintering (heating) two types of copper powder (see Exercise 5.152), the density function for Y1, the volume proportion of solid copper in a sample, was given by 6yi (1 – yı), 0< yı < 1, fi(vi) = {0 elsewhere. The density function for Y2, the proportion of type A crystals among the solid copper, was given as | 3y², 0

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 67E
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Could you please help solve the question following the below requirements (i) finding the distribution of a function of random variable(s), using the "cdf approach" and (ii) calculating expectations using the distribution derived in (i). In the "cdf approach," we first find the cdf of the variable (function) as a probability calculation, and then get the pdf by differentation. Thanks
6.14
In a process of sintering (heating) two types of copper powder (see Exercise 5.152), the density
function for Y1, the volume proportion of solid copper in a sample, was given by
бу (1 — у), 0 У <1,
fi (yı) :
elsewhere.
The density function for Y2, the proportion of type A crystals among the solid copper, was
given as
3y, 0< y2 < 1,
f2(92) = {
elsewhere.
The variable U = Y¡Y2 gives the proportion of the sample volume due to type A crystals. If Y,
and Y2 are independent, find the probability density function for U.
Transcribed Image Text:6.14 In a process of sintering (heating) two types of copper powder (see Exercise 5.152), the density function for Y1, the volume proportion of solid copper in a sample, was given by бу (1 — у), 0 У <1, fi (yı) : elsewhere. The density function for Y2, the proportion of type A crystals among the solid copper, was given as 3y, 0< y2 < 1, f2(92) = { elsewhere. The variable U = Y¡Y2 gives the proportion of the sample volume due to type A crystals. If Y, and Y2 are independent, find the probability density function for U.
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