# Segment 24

## Calculation Problems

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

3. Reproduce the table of critical <math>\Delta\chi^2</math> values shown in slide 7.

<math> \Delta\chi^2</math> is the inverse cumulative function of the <math>\chi^2</math> 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