A laboratory receives four specimens iden- tical appearances. However, it is pos

Question

A laboratory receives four specimens iden- tical appearances. However, it is possible that (a single unknown) one of the specimens is contam inated with a toxic material. The lab must test the specimens to find the toxic specimen (if in fact one is The testing plan first put forth by the laboratory staff is to test the specimens one at a time, stopping when (and if a contaminated specimen is found. Define two random variables the number of contaminated specimens and Y -the number of specimens tested Let p PIX 0] and therefore PCX 1] (a Give the conditional distributions of Y given X 0 and X 1 for the staff's initial test ing plan. Then use them to determine the joint probability function of X and Y. Oour joint distribution will involve p, and you may sim- ply fill out tables like the accompanying ones.) rix YIX

Explanation / Answer

a)

b) EY = (1+2+3+4)*(1-p)/4 + 4p = 2.5 + 1.5p

c) Here, EY = 1p + 3(1-p) = 3 - 2p

This is less than EY for the first method if 3 - 2p < 2.5 + 1.5p

0.5 < 3.5p which is p > 1/7

y fY|X(y|0) 1 0 2 0 3 0 4 1

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.