Unifrnd generates a large number of uniform distributions. Is a part of it still uniform?
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Excuse me, I use a = unifrnd (0.2,0.550000,1); generate these 50000 random numbers that conform to (0.2,0.5) uniform distribution, and then I take 3000, for example, am = a (1:3000,:). Are these 3000 random numbers also conform to (0.2,0.5) uniform distribution? thank you!
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John D'Errico
2021-3-16
编辑:John D'Errico
2021-3-16
Short answer: Yes.
Long answer: yyyyyeeeeeessssssss.
Think of it like this: These numbers have the property of beeing iid. Independent, identically distributed. And that tells you if you take some subset of them that is not based on their value, they will still have the same distribution.
Yes, if you consider a subset where you choose only those that are less than 0.3, then they will not have the same overall distribution. But a subset chosen arbitrarily based only on index will still have the original distribution.
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John D'Errico
2021-3-16
编辑:John D'Errico
2021-3-16
"i don't understand,why this subset will not have the same overall distribution? thank you"
This is getting off-topic, based on an offhand comment I made. Sigh. If I start with a set of points, all of which are assumed to lie in the interval [0.2,0.5], and are uniformly distributed on that interval. The the population mean of that set must be 0.35. Do you agree with that?
Now I extract only the subset that lies in the sub-interval [0.2,0.3]. Can the mean of this subset possibly be larger than 0.3?
The subset chosen will be UNIFORMLY distributed still. But the distribution will not possibly be the same as the original set, since the mean is different.
Yes, you can estimate the relative fraction of that set that lies less than 0.3, using the formula you show. That will not be the exact fraction in general, because this is a randomly generated set.
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