A random sample $X_{1}, \ldots, X_{36}$ is drawn from the Normal distribution with mean 0 and standard deviation 1/3. Let $S=\sum_{i=1}^{36} X_{i}$ and $Q=\sum_{i=1}^{36} X_{i}^{2}$. (a) Relate the...

$A random sample $X_{1}, \ldots, X_{36}$ is drawn from the Normal distribution with mean 0 and standard deviation 1/3. Let $S=\sum_{i=1}^{36} X_{i}$ and $Q=\sum_{i=1}^{36} X_{i}^{2}$. (a) Relate the distributions of $$$ and $Q$ to standard tabulated distributions, and find their means and variances. (b) Find the values of $a$ and $b$ so that $\mathbb{P}(S<a)=\mathbb{P}(Q<b)=0.9$. SP. JG. 431 $

Extracted text: A random sample $X_{1}, \ldots, X_{36}$ is drawn from the Normal distribution with mean 0 and standard deviation 1/3. Let $S=\sum_{i=1}^{36} X_{i}$ and $Q=\sum_{i=1}^{36} X_{i}^{2}$. (a) Relate the distributions of $$$ and $Q$ to standard tabulated distributions, and find their means and variances. (b) Find the values of $a$ and $b$ so that $\mathbb{P}(S

Jun 09, 2022

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A random sample $X_{1}, \ldots, X_{36}$ is drawn from the Normal distribution with mean 0 and standard deviation 1/3. Let $S=\sum_{i=1}^{36} X_{i}$ and $Q=\sum_{i=1}^{36} X_{i}^{2}$. (a) Relate the...

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