# The central limit theorem : Introductory video

#### Before watching the video read the questions below. As you watch the video try to answer them

# Questions

- Explain the scope of the central limit theorem. What do we want to know about the sum of a set of random variables
- State the central limit theorem, ensuring that you define all the terms within the equation.
- Explain the rationale for writing the central limit theorem without the limit sign
- In order for the central limit theorem to have any predictive value what must we be able to say about the expectation and variance of our random variable.
- Explain what we mean by a confidence limit and the meanings of the symbols $\epsilon$ and $p_c$ that are introduced in the video.
- Explain in your own words why $p_c = 2\Phi\left( \frac{ \epsilon}{\sigma / \sqrt{n}} \right) - 1$
- If I perform 20 measurements of some random quantity $X$ how many of my measurements would I expect to lie within the 95 % confidence interval.