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a)Let x be number of hours to catch a fish | a)Let x be number of hours to catch a fish | ||
| − | 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=3 | + | plug in numbers: E[x]=1 (given) a=3 |
| − | so we get: | + | so we get: |
| − | Pr[take 3 hours to catch a fish]= Pr[x>=3]<=(1/3) | + | Pr[take 3 hours to catch a fish]= Pr[x>=3]<=(1/3) |
b)Pr[not catch any fish in 2 hours] | b)Pr[not catch any fish in 2 hours] | ||
| − | = 1 - Pr[catch fish in 2+ hours] | + | = 1 - Pr[catch fish in 2+ hours] |
| − | = 1 - (Pr[x>=2]<=(1/2)) | + | = 1 - (Pr[x>=2]<=(1/2)) |
| − | >=(1/2) | + | >=(1/2) |
Revision as of 08:05, 3 November 2008
a)Let x be number of hours to catch a fish
Pr[x>=a]<=(E[x]/a) <- def of markov inqeuality plug in numbers: E[x]=1 (given) a=3 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)
