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Category > Statistics Posted 06 May 2017 My Price 3.00

Show that the median of a sample of size 2n + 1

Show that the median of a sample of size 2n + 1 from a uniform distribution on (0, 1) has a beta distribution with parameters (n + 1, n + 1).

 

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Alpha Geek
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Status NEW Posted 06 May 2017 04:05 PM My Price 3.00

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file 1494089315-Answer.docx preview (147 words )
S-----------how----------- th-----------at -----------the----------- me-----------dia-----------n o-----------f a----------- sa-----------mpl-----------e o-----------f s-----------ize----------- 2n----------- + -----------1 f-----------rom----------- a -----------uni-----------for-----------m d-----------ist-----------rib-----------uti-----------on -----------on -----------(0,----------- 1)----------- ha-----------s a----------- be-----------ta -----------dis-----------tri-----------but-----------ion----------- wi-----------th -----------par-----------ame-----------ter-----------s (-----------n +----------- 1,----------- n -----------+ 1-----------). ----------- So-----------lut-----------ion-----------: ----------- Le-----------t X----------- de-----------not-----------e t-----------he -----------med-----------ian----------- of----------- th-----------e i-----------nde-----------pen-----------den-----------t a-----------nd -----------ide-----------nti-----------cal-----------ly -----------dis-----------tri-----------but-----------ed -----------ran-----------dom----------- va-----------ria-----------ble-----------s X-----------1, -----------. .----------- . -----------, X-----------2n+-----------1. -----------Con-----------sid-----------er -----------equ-----------ati-----------on -----------6.2----------- on----------- pa-----------ge -----------272-----------. B-----------y r-----------epl-----------aci-----------ng -----------n w-----------ith----------- 2n----------- + -----------1 a-----------nd -----------by -----------cho-----------osi-----------ng -----------j =----------- n -----------+ 1-----------, w-----------e g-----------et -----------tha-----------t t-----------he -----------pro-----------bab-----------ili-----------ty -----------den-----------sit-----------y f-----------unc-----------tio-----------n o-----------f X----------- is----------- fX-----------(x)----------- = -----------(2n----------- + -----------1)!----------- n!-----------n! -----------(F(-----------x))-----------n
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