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Category > Statistics Posted 05 Jun 2017 My Price 3.00

Suppose we flip a fair coin repeatedly

Suppose we flip a fair coin repeatedly. Let Xi equal 1 if flip i was heads (H) and 0 otherwise. Let N denote the number of flips needed until H has occurred 100 times. Is N independent of the random sequence X1, X2,...? Define Y = X1+···+ XN. Is Y an ordinary random sum of random variables? What is the PMF of Y?

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

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file 1496681583-Answer.docx preview (140 words )
S-----------upp-----------ose----------- we----------- fl-----------ip -----------a f-----------air----------- co-----------in -----------rep-----------eat-----------edl-----------y. -----------Let----------- Xi----------- eq-----------ual----------- 1 -----------if -----------fli-----------p i----------- wa-----------s h-----------ead-----------s (-----------H) -----------and----------- 0 -----------oth-----------erw-----------ise-----------. L-----------et -----------N d-----------eno-----------te -----------the----------- nu-----------mbe-----------r o-----------f f-----------lip-----------s n-----------eed-----------ed -----------unt-----------il -----------H h-----------as -----------occ-----------urr-----------ed -----------100----------- ti-----------mes-----------. I-----------s N----------- in-----------dep-----------end-----------ent----------- of----------- th-----------e r-----------and-----------om -----------seq-----------uen-----------ce -----------X1,----------- X2-----------,..-----------.? -----------Def-----------ine----------- Y -----------= X-----------1+Â-----------·Â·-----------·+----------- XN-----------. I-----------s Y----------- an----------- or-----------din-----------ary----------- ra-----------ndo-----------m s-----------um -----------of -----------ran-----------dom----------- va-----------ria-----------ble-----------s? -----------Wha-----------t i-----------s t-----------he -----------PMF----------- of----------- Y?----------- A-----------nsw-----------er ----------- Of----------- co-----------urs-----------e N----------- is----------- no-----------t i-----------nde-----------pen-----------den-----------t o-----------f t-----------he -----------seq-----------uen-----------ce -----------(X_-----------i).----------- Su-----------ffi-----------ce -----------to -----------say----------- th-----------at -----------if -----------we -----------get----------- X1-----------=X2-----------=X3-----------=..-----------.=X-----------99=-----------X10-----------0=1-----------
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