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Consider an experiment where you toss a coin as often as necessary to turn up one...

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Basic Math

Consider an experiment where you toss a coin as often asnecessary to turn up one head.Suppose that the probability ofhaving a tail is p(obviously probability of a head is 1?p).Assumeindependence between tosses.a) State the sample space.

b) Let X be the number of tosses needed to get one head. What isthe support (possible values ofX)?

c) FindP(X= 1),P(X= 2) andP(X= 3).

d) Deduce the pmf of X from part c).

Answer & Explanation Solved by verified expert
4.2 Ratings (566 Votes)
aLet H denote head and T denote tailWe need to find the sample space for the experiment where wecontinuously toss the coin until we get a head Before that firsthead comes we need to have only tails as our outcomeNow we could get a head on the first toss in which case theevent will be Hor we could get a head on the second    See Answer
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