Help with a math problem

HarryCaray · Feb 19, 2010

I'm normally very good with math, but can't remember how to solve this word problem.

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oNotOptimizeForBrowser/> <m:mathPr> <m:mathFont m:val="Cambria Math"/> <m:brkBin m:val="before"/> <m:brkBinSub m:val="--"/> <m:smallFrac m:val="off"/> <m:dispDef/> <m:lMargin m:val="0"/> <m:rMargin m:val="0"/> <m:defJc m:val="centerGroup"/> <m:wrapIndent m:val="1440"/> <m:intLim m:val="subSup"/> <m:naryLim m:val="undOvr"/> </m:mathPr></w:WordDocument> </xml><![endif]--><style>  </style>[FONT=&quot]A web site has 900 pages, each with 5 entries on it. I've been hitting the random button which randomly generates 15 entries (the same entry can show up more than once, the site has no memory as to what you've seen, i.e. WITH replacement). There is an average of one new entry per hour onto the site.

I am hitting Random an average of once per 0.5 hrs on the site every day (so I see an average of 240 entries per day). Assuming I start at midnight on Feb 1 and only use the randomization, at what date and time (rounded to the nearest half hour) is it statistically certain that I've seen every text on the site?

SOMEONE HELP (and please explain how you did it).

Hour 0: 4,500 entries
Hour 1: 4,501 entries, and I have seen up to 30 unique entries
etc.

Don't remember where to go from here.
[/FONT]

festeringZit · Feb 19, 2010

You have to define what you mean by statistically certain, because
there is a chance (almost infinitely small) that you would
never see every text.

The question is better posed as:

How long before I can be > 95% ( or 99% for example ) certain to have seen all texts.

festeringZit · Feb 19, 2010

[FONT=&quot]"I am hitting Random an average of once per 0.5 hrs on the site every day (so I see an average of 240 entries per day)."[/FONT]

Wouldn't this be:

2*24*15 = 720 entries seen per day?

cincy_ · Feb 19, 2010

You will never be certain that you have seen every entry.

If you draw a graph for the probability, you will see that it is asymptotic.

As time approaches infinity, probability approaches 1.

cincy_ · Feb 19, 2010

Like zit says, HOW SURE do you want to be?

... and don't say 100%.

HarryCaray · Feb 23, 2010

Yeah that wasn't the right way to say it. Let's say 99%. I understand it will never hit 1.

HarryCaray · Feb 23, 2010

festeringZit said:
[FONT=&quot]"I am hitting Random an average of once per 0.5 hrs on the site every day (so I see an average of 240 entries per day)."[/FONT]

Wouldn't this be:

2*24*15 = 720 entries seen per day?

Yeah, sorry, the original random button used to display 5 at a time and now it displays 15. Forgot to change that part of it.

JDeuce · Feb 24, 2010

Just did a problem very similar to this in my quantitative stats class.

I'll work through it tomorrow for both 95 and 99 percent certainty.

HarryCaray · Feb 24, 2010

JDeuce said:
Just did a problem very similar to this in my quantitative stats class.

I'll work through it tomorrow for both 95 and 99 percent certainty.

Thanks. I remember doing problems like this but I can't remember how to do it.

HarryCaray · Feb 26, 2010

JDeuce, help a brother out!

HarryCaray · Feb 28, 2010

Bump...no one on this forum can answer this?

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