AP Statistics : How to find the chi-square distribution

Study concepts, example questions & explanations for AP Statistics

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Example Questions

Example Question #1 : How To Find The Chi Square Distribution

\(\displaystyle Y\) follows a chi-squared distribution with \(\displaystyle 6\) degrees of freedom and \(\displaystyle X_1\) through \(\displaystyle X_n\) are independent standard normal variables.

If \(\displaystyle Y = \sum_{i = 1}^{n}X_i^2\), what is \(\displaystyle n\)?

Possible Answers:

\(\displaystyle 4\)

\(\displaystyle 7\)

\(\displaystyle 5\)

\(\displaystyle 8\)

\(\displaystyle 6\)

Correct answer:

\(\displaystyle 6\)

Explanation:

Use the fact that the sum of \(\displaystyle n\) squared standard and independent normal variables follows a chi-squared distribution with \(\displaystyle n\) degrees of freedom.

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