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Category > Statistics Posted 30 May 2017 My Price 3.00

Let Y1 and Y2 be independent random variables that are both uniformly distributed

 

 
 

 

Let Y1 and Y2 be independent random variables that are both uniformly distributed on the interval (0,1) find P(Y1 < 2*Y2 | Y1 < 3*Y2)
 
 

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Alpha Geek
(8)
Status NEW Posted 30 May 2017 08:05 AM My Price 3.00

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file 1496134131-Answer.docx preview (83 words )
L-----------et -----------Y1 -----------and----------- Y2----------- be----------- in-----------dep-----------end-----------ent----------- ra-----------ndo-----------m v-----------ari-----------abl-----------es -----------tha-----------t a-----------re -----------bot-----------h u-----------nif-----------orm-----------aly----------- di-----------str-----------but-----------ed -----------on -----------the----------- in-----------ter-----------val----------- (0-----------,1)----------- fi-----------nd -----------P(Y-----------1 &-----------amp-----------;lt-----------; 2-----------*Y2----------- | -----------Y1 -----------&am-----------p;l-----------t; -----------3*Y-----------2) ----------- Ma-----------y 0-----------6 2-----------012----------- 10-----------:32----------- PM----------- A-----------nsw-----------er ----------- Th-----------e e-----------ven-----------t [-----------(Y1-----------&am-----------p;l-----------t;2-----------*Y2-----------) o-----------r (-----------Y1&-----------amp-----------;lt-----------;3*-----------Y2)-----------] i-----------s t-----------he -----------sam-----------e a-----------s t-----------he -----------eve-----------nt -----------(Y1-----------&am-----------p;l-----------t;3-----------*Y3-----------). -----------Thi-----------s i-----------s b-----------eca-----------use----------- th-----------e e-----------ven-----------t (-----------Y1&-----------amp-----------;lt-----------;2*-----------Y2)----------- co-----------res-----------pon-----------ds -----------to -----------poi-----------nts----------- ab-----------ove----------- th-----------e l-----------ine----------- Y2-----------=(1-----------/2)-----------Y1 -----------in -----------the----------- Y1-----------, Y-----------2 p-----------lan-----------e, -----------and----------- in-----------sid-----------e t-----------he -----------uni-----------t s-----------qua-----------re,----------- an-----------d t-----------he -----------eve-----------nt -----------(Y1-----------&am-----------p;l-----------t;3-----------*Y2-----------)
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