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...

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

Extracted 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,="">< 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="">