A X^2v will look very much like a normal distribution for large values of y (the

Question

A X^2v will look very much like a normal distribution for large values of y (the degrees of freedom). Which of the following statements is the best explation as to why this makes sense? A X^2v distribution is related to the sample variance S^2 of a sample from a normal distribution, and functions of random variables with normal distributions will also be normal. A X^2v distribution is a model for a sum of (roughly) v random variables that are independent, and a sum of a large number of random variables will tend to follow a normal distribution A X^2v distribution is related to the sample variance S^2 of a sample from a normal distribution, and when the sample size is large enough S^2 will be a very good approximation to the population variance sigma^2 , with only a small chance of being wrong in either direction. A X^2v, distribution is an important part of the more important t distribution, which will be symmetric and bell shaped and therefore approximately normal.

Explanation / Answer

Option C is the better option as the chi-squared distribution with k degrees of freedom is the distribution of a sum of the squares of k independent standard normal random variables. So, as the sample size is larger, implies more independent standard normal random variables, the sample variance approximates to population variance

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