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Chapter 1: Problem 4

Give one example each of sampling with and sampling without replacement.

Short Answer

Expert verified
In a scenario of sampling with replacement, we could draw 'red', 'red', 'blue' from a bag of three colored balls (red, blue, green) because after observing a ball's color, it's put back in the bag. In sampling without replacement, we could draw 'red', 'blue', and 'green' in sequence from the same bag, but we can't draw the 'red' ball again after it's first drawn because it's not replaced.

Step by step solution

01

Example of Sampling with Replacement

An instance of sampling with replacement could include a bag filled with three colored balls: red, blue, and green. We draw a ball, note down its color, and then put it back into the bag before drawing again. So, for example, we could encounter the sequence 'red', 'red', 'blue', which is possible as each draw is independent and the ball is returned after each draw.
02

Example of Sampling without Replacement

On the flip side, an example of sampling without replacement could be the same bag with three colored balls. This time, after drawing a ball, we don鈥檛 put it back. Therefore, if we draw 'red', 'blue', and 'green' in sequence, we can't draw the 'red' ball again after the first draw because it wasn't replaced.

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