# Eleisha's Segment 24: Goodness of Fit

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