3 ms·
I have a question that is only tangentially related to this so feel free to ignore. Say I flip 50 fair coins, P(heads)=P(tails)=0.5, 10 times each a day for 10
by nonbel 11y ago
I have a question that is only tangentially related to this so feel free to ignore.
Say I flip 50 fair coins, P(heads)=P(tails)=0.5, 10 times each a day for 100 days. For each coin we have 100 records like HTHTHHTTHT. Now I count the number of tails (5 in the example) for each day for each coin. So each coin has a record with length 100 like [5, 8, 5, ...,6]. Now I can calculate the variance of these values for each coin and end up with 50 variances. What do we expect the distribution of these variances to look like?
- GFK_of_xmaspast 11y agoApproximately normal. See stuff like : http://onlinestatbook.com/2/sampling_distributions/samp_dist_p.html http://onlinestatbook.com/2/sampling_distributions/samp_dist...
- nonbel 11y agoI am asking how to calculate the expected distribution of sample variances, not sample means.
- mccourt 11y agoI need a bit of clarification here. In the list of length 100, each entry in that list is a binomial random variable X~Binom(10, .5). The variance of each of these binomials is Var(X) = 10(.5)(.5) = 2.5. But I don't think that's the variance you're talking about. Do you mean the sample variance of the list of length 100? I'm sure that we can figure that out too (or at least what it should look like) but I want to confirm that's the variance you are interested in. Off the top of my head, I think this sample variance should have a roughly Chi-Square distribution, since Binom(10, .5) is close to normal (sort of). In the Wikipedia article, it explains how Chi-Square can be expressed a sum of normals squared (https://en.wikipedia.org/wiki/Chi-squared_distribution https://en.wikipedia.org/wiki/Chi-squared_distribution). I could maybe figure out the actual distribution if you really need it. Then you ask what should the distribution look like? Is this answered by the answer above, or did you mean something related to the 50 samples in particular?
- nonbel 11y agoThanks, I'm wondering how to calculate the distribution of sample variances. Yes, each variance is calculated from the list of 100 counts of #tails. It's just something that has bothered me for awhile.