Sampling Without Replacement (VCE SSCE Mathematical Methods): Flashcards

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Sampling without replacement
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Sampling without replacement definition

Selecting items without returning them before next selection

Probability after each selection (sampling w/o replacement)

Changes because composition of group changes

Sampling w/o replacement: events are

Dependent (not independent)

Tree diagram: probability of complete path

Multiply along the branches

Tree diagram: same outcome via different paths

Add across different paths

Hypergeometric distribution

Sampling w/o replacement from finite pop. with 2 types

Probability distribution verification

All probabilities must sum to 1

(nr)\binom{n}{r} meaning

Number of ways to select rr objects from nn objects

Formula: Pr(X=x)\Pr(X=x) using combinations

favourable outcomestotal outcomes\frac{\text{favourable outcomes}}{\text{total outcomes}}

Hypergeometric: population characteristics

Finite, two distinct categories, sampled w/o replacement

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