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Category > Statistics Posted 07 May 2017 My Price 3.00

The random variables X and Y are independent

The random variables X and Y are independent and uniformly distributed in interval (0.1). Determine the probability that their product XY is less than 1/2.

 

 

 

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Status NEW Posted 07 May 2017 05:05 PM My Price 3.00

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file 1494178432-Answer.docx preview (40 words )
T-----------he -----------ran-----------dom----------- va-----------ria-----------ble-----------s X----------- an-----------d Y----------- ar-----------e i-----------nde-----------pen-----------den-----------t a-----------nd -----------uni-----------for-----------mly----------- di-----------str-----------ibu-----------ted----------- in----------- in-----------ter-----------val----------- (0-----------.1)-----------. D-----------ete-----------rmi-----------ne -----------the----------- pr-----------oba-----------bil-----------ity----------- th-----------at -----------the-----------ir -----------pro-----------duc-----------t X-----------Y i-----------s l-----------ess----------- th-----------an -----------1/2-----------. ----------- A-----------nsw-----------er:----------- -----------Dis-----------tan-----------ce -----------bet-----------wee-----------n x----------- an-----------d y----------- is----------- Mo-----------dul-----------ous----------- (y------------x)----------- = -----------0.5----------- y -----------= x-----------+0.-----------5 T-----------hat-----------'s -----------the----------- R-----------2R2----------- i-----------nte-----------rva-----------l:Â----------- ?[-----------0;1-----------]×-----------[ma-----------x{0-----------,x------------0.5-----------};m-----------in{-----------1,x-----------+0.-----------5}]-----------?[0-----------;1]-----------×[-----------max-----------{0,-----------x-0-----------.5}-----------;mi-----------n{1-----------,x+-----------0 -----------
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