Question

What is the relationship between sampling without replacement and independence and how does that affect the computation of the probabilities of two successive events? How bout sampling with replacement; does that lead to independent or dependent outcomes?

Answer #1

For computing probabilities of **two independent**
evevts which are occuring successively we at first find the
**probabilities of each of the events separately** and
then multiply them to get
the overall probability.

Sampling **without replacement** leads to a
**dependent case** beacause the sample which is
selected in the first draw has an effect on the sample selected in
the second draw.Therefore
sampling without replacement leads to dependent
outcomes.

Now in sampling **with replacement** the outcomes
are **independent.** the sample selected in the first
draw is again **returned** and then for the
**second selection also we obtain the same sample
space**, that we had in the first draw.

How to prove that sampling without replacement is exchangeable,
but not independent.

what does it mean to when sampling is done without
replacement?

true or false A moderating variable does not affect the strength
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of one? type, while the remaining B objects are of the other? type,
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1.
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In observational studies, the observed relationship
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For the two hypotheses below:
a. Think up a plausible alternative casual
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b. Describe how this variable might affect the
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