16 lines
1.2 KiB
Markdown
16 lines
1.2 KiB
Markdown
(Ch 18, stat 1040)
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The probability histogram for the sum of
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the draws looks like the normal curve, even if the tickets in
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the box are not normally distributed, as long as the draws
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are sufficiently large.
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Probability histograms represent *chance*. Each class interval represents the probability an event would occur. As the number of repetitions increases, the closer the graphed data will appear to the calculated probability histogram.
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The probability curve for the *sum of draws* will approximately follow the normal curve if the number of draws is large enough, even if the tickets in the box *do not follow the normal curve.
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When applying statistics to sums, it's usually in the form of *how much do we think the sum will add up to*, then compared against what it actually adds up to. The $EV_{sum}$ is used for for the estimated sum of all events. The $SE_{sum}$ refers to the standard error of the sum, or how much you expect the guess to be off by. This can be thought of like the standard deviation.
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If the box is not uniform, the graph will not follow the normal curve as closely.
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The central limit theorem says that if a distribution is not normal, you can still follow the normal distribution if the number of draws is large, and the draws are random. |