How does sampling with or without replacement affect probabilities?

How does sampling with or without replacement affect probabilities?

Sampling With or Without Replacement 1 Effect on Probabilities. To see how we handle replacement affects the calculation of probabilities, consider the following example question. 2 Population Sizes. There are some situations where sampling with or without replacement does not substantially change any probabilities. 3 Other Applications.

What is the probability of selecting a female with or without replacement?

If we sample with replacement, then the probability of choosing a female on the first selection is given by 30000/50000 = 60%. The probability of a female on the second selection is still 60%. The probability of both people being female is 0.6 x 0.6 = 0.36. If we sample without replacement then the first probability is unaffected.

What happens if I sample two without replacement?

If I sample two without replacement, then I first pick one (say 14). I had a 1/7 probability of choosing that one. Then I pick another. At this point, there are only six possibilities: 12, 13, 15, 16, 17, and 18. So there are only 42 different possibilities here (again assuming that we distinguish between the first and the second.)

What is the covariance between sampling with and without replacement?

Practically, this means that what we get on the first one doesn’t affect what we get on the second. Mathematically, this means that the covariance between the two is zero. In sampling without replacement, the two sample values aren’t independent.

What do we do with the individual after sampling?

This question that arises when sampling is, “After we select an individual and record the measurement of attribute we’re studying, what do we do with the individual?” We can replace the individual back into the pool that we are sampling from. We can choose to not replace the individual.

When do you sample with or without replacement?

For this reason, many times even though we sample without replacement, we treat the selection of each individual as if they are independent of the other individuals in the sample. There are other instances where we need to consider whether to sample with or without replacement. On example of this is bootstrapping.