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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 |
| − | plug in numbers: E[x]=1 (given) a= | + | Let x be number of hours to catch a fish |
| − | so we get: | + | plug in numbers: E[x]=1 (given) a=3b (given) |
| − | Pr[take 3 hours to catch a fish]= Pr[x>=3]<=(1/3) | + | so we get: |
| − | b)Pr[not catch any fish in 2 hours] | + | Pr[take 3 hours to catch a fish]= Pr[x>=3]<=(1/3) |
| − | = 1 - Pr[catch fish in 2+ hours] | + | b) |
| − | = 1 - (Pr[x>=2]<=(1/2)) | + | Pr[not catch any fish in 2 hours] |
| − | >=(1/2) | + | = 1 - Pr[catch fish in 2+ hours] |
| + | = 1 - (Pr[x>=2]<=(1/2)) | ||
| + | >=(1/2) | ||
Latest revision as of 08:06, 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)
