# Segment 24

## Calculation Problems

1. Let $X$ be an R.V. that is a linear combination (with known, fixed coefficients $\alpha_k$) of twenty $N(0,1)$ deviates. That is, $X = \sum_{k=1}^{20} \alpha_k T_k$ where $T_k \sim N(0,1)$. How can you most simply form a t-value-squared (that is, something distributed as $\text{Chisquare}(1)$ from $X$? For some particular choice of $\alpha_k$'s (random is ok), generate a sample of $x$'s, plot their histogram, and show that it agrees with $\text{Chisquare}(1)$.

3. Reproduce the table of critical $\Delta\chi^2$ values shown in slide 7.

$\Delta\chi^2$ is the inverse cumulative function of the $\chi^2$ distribution with it's degree of freedom.

chi2.pph(q,df)


where q is the distribution's confidence leven and df the degree of freedom