File - AP Statistics
... 10. A survey asks a random sample of 500 adults in Ohio if they support an increase in the state sales tax from 5% to 6%, with the additional revenue going to education. Let denote the proportion in the sample who say they support the increase. Suppose that 53% of all adults in Ohio support the incr ...
... 10. A survey asks a random sample of 500 adults in Ohio if they support an increase in the state sales tax from 5% to 6%, with the additional revenue going to education. Let denote the proportion in the sample who say they support the increase. Suppose that 53% of all adults in Ohio support the incr ...
1.017 Class 10: Common Distributions
... Suppose that [zL, zU] is selected so that the probability that z lies above the interval is the same as the probability that it lies below the interval. This gives a two-sided interval [zL, zU] for z: P[ z (aˆ , a ) z L ] Fz ( z L ) ...
... Suppose that [zL, zU] is selected so that the probability that z lies above the interval is the same as the probability that it lies below the interval. This gives a two-sided interval [zL, zU] for z: P[ z (aˆ , a ) z L ] Fz ( z L ) ...
Chapter 2: The Normal Distributions 2.1 Density Curves and the
... 3. Where is the median of a density curve located? The median is the equal-areas point. Half the area under the curve is to the left, the other half of the area is to the right. 4. Where is the mean of a density curve located? The mean is the balance point of the density curve. The mean and median a ...
... 3. Where is the median of a density curve located? The median is the equal-areas point. Half the area under the curve is to the left, the other half of the area is to the right. 4. Where is the mean of a density curve located? The mean is the balance point of the density curve. The mean and median a ...
1.3 Density curves p50 •Some times the overall pattern of a large
... •Some times the overall pattern of a large number of observations is so regular that we can describe it by a smooth curve. • It is easier to work with a smooth curve, because the histogram depends on the choice of classes. •Density Curve (p52) Density curve is a curve that - is always on or above th ...
... •Some times the overall pattern of a large number of observations is so regular that we can describe it by a smooth curve. • It is easier to work with a smooth curve, because the histogram depends on the choice of classes. •Density Curve (p52) Density curve is a curve that - is always on or above th ...
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... Example A soldier try to shot a bomber with probability 0.02 that he can hit the target, suppose the he independently give the target 400 shots, try to determine the probability that he hit the target at least for twice. Answer Let X represent the number that hit the target in 400 shots Then X～B(40 ...
... Example A soldier try to shot a bomber with probability 0.02 that he can hit the target, suppose the he independently give the target 400 shots, try to determine the probability that he hit the target at least for twice. Answer Let X represent the number that hit the target in 400 shots Then X～B(40 ...
Central limit theorem
In probability theory, the central limit theorem (CLT) states that, given certain conditions, the arithmetic mean of a sufficiently large number of iterates of independent random variables, each with a well-defined expected value and well-defined variance, will be approximately normally distributed, regardless of the underlying distribution. That is, suppose that a sample is obtained containing a large number of observations, each observation being randomly generated in a way that does not depend on the values of the other observations, and that the arithmetic average of the observed values is computed. If this procedure is performed many times, the central limit theorem says that the computed values of the average will be distributed according to the normal distribution (commonly known as a ""bell curve"").The central limit theorem has a number of variants. In its common form, the random variables must be identically distributed. In variants, convergence of the mean to the normal distribution also occurs for non-identical distributions or for non-independent observations, given that they comply with certain conditions.In more general probability theory, a central limit theorem is any of a set of weak-convergence theorems. They all express the fact that a sum of many independent and identically distributed (i.i.d.) random variables, or alternatively, random variables with specific types of dependence, will tend to be distributed according to one of a small set of attractor distributions. When the variance of the i.i.d. variables is finite, the attractor distribution is the normal distribution. In contrast, the sum of a number of i.i.d. random variables with power law tail distributions decreasing as |x|−α−1 where 0 < α < 2 (and therefore having infinite variance) will tend to an alpha-stable distribution with stability parameter (or index of stability) of α as the number of variables grows.