Q56Section I (Objective (Q1–Q80))56 of 80

Distribution Theory — degrees of freedom under linear restrictions

Let $(X_1, X_2, …, X_{53})$ be a random sample from $N(0, 1)$ distribution. If for some $\alpha$ 's, $\beta$ 's and $\gamma$ 's, $\sum_{i=1}^{53}\alpha_iX_i = 0$ , $\sum_{i=1}^{53}\beta_iX_i = 0$ and $\sum_{i=1}^{53}\gamma_iX_i = 0$ , then the distribution of $\sum_{i=1}^{53}X_i^2$ , is:

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