Question

1. In this problem, you are going to numerically verify that the Central Limit Theorem is valid even when sampling from non-normal distributions. Suppose that a component has a probability of failure described by a Weibull distri- bution. Let X be the random variable that denotes time until failure; its probability density is: for a 2 0, and zero elsewhere. In this problem, assume k 1.5, 100 a) Simulate drawing a set of N-20 sample values, repeated over M 200 samples, b) Plot the histogram of all 4,000 samples to verify that your samples represent the c) Compute the means associated with each of the M samples and plot a histogram from this component using the inverse sampling method pdf above. of the sample means. Does this histogram appear to be normally distributed?

Answer 1

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