Test 1 with Solution Key - Statistics for Engineering | STAT 4705, Exams of Statistics

Download Test 1 with Solution Key - Statistics for Engineering | STAT 4705 and more Exams Statistics in PDF only on Docsity! 44 STAT 4705 Test I February 20, 2004 Nar | 1. Some products can have visible defects and invisible defects. For example, a radio might have a damaged power cord that can be easily detected by visual examination, or a defective switch that can only by detected when the radio is turned on and tested. Suppose that in a box containing 24 radios, 1 radio has only visible defects, 2 radios have only invisible defects, 3 radios have both visible and invisible defects, and the remaining 18 radios have no defects. Suppose that 3 radios are selected at random from the box for inspection. (a) Find the probability that there are no defects that are visible in the 3 radios selected for inspection. . ' ee fi ena Cro > ee CB Ne suse / at = OY (a) Given that there are no visible defects in the 3 radios selected, find the conditional probability that there are no invisible defects ? (ne wads \ No pe) {yen wo viewbhe Sa teftet = to ob eg Sle tte Wo wwieie oe 1G 2) 2. Let X represent the time (in years) until a component fails, and let Y represent the level of c 4 stress on the component. For convenience, the stress level has been scaled so that the values for Y fall between 0 and 1, Xand Y are continuous random variables with joint density fy,yzl-xt+y, OSx<1,0< ysl. (a) Find E(%), the expected stress level. 1 Sax 44 84 Ets (b) Find the conditional probability that the component will fail in the first 6 months (0.5 years), given that Y= 0.3. . = ley \3 € dyly ds FG? < Fey 2 § (eur 3 dy ® Ful Za “S ~ xT 3x |, 2