Theory about applications - [TA7]

In the previous application we generated a normal variate using the Box-Muller method, and computed various distributions using it.
We will now briefly overview the distributions that were computed.

Normal Distribution

First of all we simply sampled the normal variate as is, generating and plotting a histogram that represents the normal distribution.

Chi-Squared Distribution

We then computed the chi-squared distribution by squaring the normal variate.

Cauchy Distribution

We then computed the Cauchy distribution by dividing the normal variate $X$ by another normal variate $Y$.

Student’s t-Distribution

The Student’s t-distribution is a probability distribution that is used in the hypothesis testing of small sample data sets.
It can be computed by dividing a normal variate $X$ by the square root of a chi-squared variate $Y$ divided by its degrees of freedom.

F-Distribution

Finally we computed a F-distribution by dividing two chi-squared variates $X$ and $Y$ by their degrees of freedom.

For a visual representation of the distributions, see the post regarding the application 13.

Sources

• https://en.wikipedia.org/wiki/Normal_distribution
• https://en.wikipedia.org/wiki/Chi-squared_distribution