(Brian Thomas rhea hw5. I aplogize that this is a few hours past due.) |
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<math>X_i</math> is geom<math>(\frac{n - i + 1}{n})</math> | <math>X_i</math> is geom<math>(\frac{n - i + 1}{n})</math> | ||
| − | E[# needed]=<math>\sum_{i=1}^n E[Xi] = \sum_{i=1}^n \frac{n - i + 1 | + | E[# needed]=<math>\sum_{i=1}^n E[Xi] = \sum_{i=1}^n \frac{n}{n - i + 1}</math> |
I attempted to plug this into matlab's symbolic calculator, but the answer didn't come out to anything I understood. | I attempted to plug this into matlab's symbolic calculator, but the answer didn't come out to anything I understood. | ||
Also, note for geom(p), variance is <math>\frac{1-p}{p^2}</math>. I don't think we can simply add all the variances up; does anybody have a better idea? | Also, note for geom(p), variance is <math>\frac{1-p}{p^2}</math>. I don't think we can simply add all the variances up; does anybody have a better idea? | ||
Latest revision as of 18:25, 6 October 2008
Virgil -- I don't see you contributing anything useful. Please use the wiki to help others along with the problems instead of complaining.
In addition, to Henry: I agree with your idea and your conclusion. We can expand a small amount from your idea by generalizing the forumla for $ X_i $:
$ X_i $ is geom$ (\frac{n - i + 1}{n}) $
E[# needed]=$ \sum_{i=1}^n E[Xi] = \sum_{i=1}^n \frac{n}{n - i + 1} $
I attempted to plug this into matlab's symbolic calculator, but the answer didn't come out to anything I understood.
Also, note for geom(p), variance is $ \frac{1-p}{p^2} $. I don't think we can simply add all the variances up; does anybody have a better idea?
