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a) | a) | ||
Pr[x>=a]<=(E[x]/a) <- def of markov inqeuality | Pr[x>=a]<=(E[x]/a) <- def of markov inqeuality | ||
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Let x be number of hours to catch a fish | Let x be number of hours to catch a fish | ||
plug in numbers: E[x]=1 (given) a=3b (given) | plug in numbers: E[x]=1 (given) a=3b (given) | ||
Latest revision as of 07:06, 3 November 2008
a)
Pr[x>=a]<=(E[x]/a) <- def of markov inqeuality Let x be number of hours to catch a fish plug in numbers: E[x]=1 (given) a=3b (given) so we get: Pr[take 3 hours to catch a fish]= Pr[x>=3]<=(1/3)
b)
Pr[not catch any fish in 2 hours] = 1 - Pr[catch fish in 2+ hours] = 1 - (Pr[x>=2]<=(1/2)) >=(1/2)
