Question

Let X be the proportion of impurities in chemical product. The distribution of has the following p.d.f. f(x) = (0+2x+3) x + (1-x)

Answer 1

Let I be the proportion of impurile in a chemical products. The poof of follow, f@) = (0+2)(043)©*(1-x2) • 0<x</ as

then, Elx) = fx f(x) de o 9-x) dx 그 こ = @+3)(C+2) - (0+3)@12) Bela @13,2) = @43) (0+2) (1043) 17 1(0+5) (0+3)(0+).) @+41(0+3) Cotz 6th Heuer E(x) = ceth ota

Let Mertar to be a random sample of size и в гирии оf chennal 2 И. We и арх Х- wra +1 Талап элeriod of шашлик з відзивід, с X: 1 5 х (84) - tta ҳ& +4х = &ға 2 % (x-1) = а. 44 x а(1-2х) (x-1) Hence method of moueats estiloctor S 0 - 5 е (О СА 2 а(1 - 28)

as ? LI Q +1 H И. n @+1 (@13) (73), 176C1-Hi) The likelihood ftuchan force LO@) = f 080 - P (43)(c+2)= 1 - 0 The logletjelihood function for cos Log (%): nlog(+3)+h log(0+2) + (0-1) Žlogai + 320g (1-25 こ Es as a

И. Exi Lorkesachialê wort Qmie ged dlog (9x): ✓ da For MLE of o, we led? И. 013 t at2 Halog (97) = 0 И. Exico + 3 ㅛ (6+3 t И 0+2 3 cetat cata Its=0 where s hoge Then, 0+2+0+3+(@2450 +6)=0 862+ o sce? Co (58+8) + 6sts 50 50st 68 + 20+5 CD s

Then? -Sata) - (445)” ( (645) E 28 Heuer MLE of a as a @ : -($+a) - Vsta)? 4ML 65+5) QS where = ر م st loga N

ot k аtе оf еде Өии, We И. and ва , n= 10, х = 0-3740/ « : hаlоq = -(- sao63 Thee neethod of moment estimate ce as ? (О. С). 3Ds | The maximum likelihood timelo 4 с С 2 6. -1:20791