I have a sample X1, X2,..., Xn that drawn from uniformly distributed population. The sample drawn without replacement. Since it depends each other (which is not i.i.d), the joint pdf is not the product of each Xi. How do I construct the joint pdf?
I do not think your question is entirely clear. If you know the distribution to be U(a,b) and you are sampling from this distribution, what is then meant by sampling without replacement? Do you mean you have a sample that is approximately uniform from which you are drawing subsamples (w/o replacement)?
The question lacks information, I think that you're talking about a simple random sampling without replacement, if so, you must meet the following requirements:
1. The sampling shape must have a sampling frame that specifies how to identify each unit in the population.
2. Also not known a priori on the possible values of Yi and other measurements associated with Yi.
3. In this case each unit is drawn with equal probability, in stages, without replacement, to have the n sample units.
For more information of the theme, you search the following words : "SIMPLE RANDOM SAMPLING WITHOUT REPLACEMENT".
HI,
In sampling without replacement, the two sample values aren't independent. Practically, this means that what we got on the for the first one affects what we can get for the second one. Mathematically, this means that the covariance between the two isn't zero. In particular, if we have a SRS (simple random sample) without replacement, from a population with variance.
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