m2_2_variation_z_scores
... their parts extremely close to this diameter in order for them to fit properly. We would assume that the average diameter of, say, 10000 parts would indeed be very close to 2.3. However, the question from a manufacturing perspective would be: How much variation is there among the parts? The manufact ...
... their parts extremely close to this diameter in order for them to fit properly. We would assume that the average diameter of, say, 10000 parts would indeed be very close to 2.3. However, the question from a manufacturing perspective would be: How much variation is there among the parts? The manufact ...
Distributions.jl Documentation
... It always returns () when s is univariate, and (length(s),) when s is multivariate. nsamples(s, A) The number of samples contained in A. See above for how multiple samples may be organized into a single array. eltype(s) The default element type of a sample. This is the type of elements of the sample ...
... It always returns () when s is univariate, and (length(s),) when s is multivariate. nsamples(s, A) The number of samples contained in A. See above for how multiple samples may be organized into a single array. eltype(s) The default element type of a sample. This is the type of elements of the sample ...
Confidence Intervals - Department of Mathematical Sciences
... (that is, S → σ), we have (by Slustky’s Theorem) that n(X n − µ)/S →N(0,1). Using this as the pivotal quantity, it follows that an approximate confidence interval for µ is S Xn ± c √ n where c is from a N(0,1) distribution. Sometimes, we don’t need to “plug-in” S for σ. If σ is a function of µ (as w ...
... (that is, S → σ), we have (by Slustky’s Theorem) that n(X n − µ)/S →N(0,1). Using this as the pivotal quantity, it follows that an approximate confidence interval for µ is S Xn ± c √ n where c is from a N(0,1) distribution. Sometimes, we don’t need to “plug-in” S for σ. If σ is a function of µ (as w ...
November 2003 examination
... In the first actuary’s simulation, a driver is selected and one year’s experience is generated. This process of selecting a driver and simulating one year is repeated N times. In the second actuary’s simulation, a driver is selected and N years of experience are generated for that driver. Which of t ...
... In the first actuary’s simulation, a driver is selected and one year’s experience is generated. This process of selecting a driver and simulating one year is repeated N times. In the second actuary’s simulation, a driver is selected and N years of experience are generated for that driver. Which of t ...
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.