| Line 1: | Line 1: | ||
| − | 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 | ||
| + | plug in numbers: E[x]=1 (given) a=3b (given) | ||
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)
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)
