Topic 3.i: Multivariate Random Variables – State and apply the Central Limit Theorem. The value \(2.326\) is nothing more than our application of the Central Limit Theorem (\(\Phi(0.99)\)). It provides a simple method for computing approximate probabilities for sums of independent random variables and helps explain the remarkable fact that the empirical frequencies of so many natural populations exhibit bell-shaped (or normal) curves.Īfter analyzing the moment generating technique, we have found that the mean \(\bar(0.99)$$ You can visit our normal distribution calculator for more on the topic. The central limit theorem definition states that the sampling distribution approximates a normal distribution as the sample size becomes larger, irrespective of the shape of the population distribution. It states that the sum of a large number of independent random variables has an approximately normal distribution. In statistics, the central limit theorem concerns sample distributions. The central limit theorem is of the most important results in the probability theory. For this learning objective, a certain knowledge of the normal distribution and knowing how to use the Z-table is assumed.
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