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  1. J

    Checking the Independence.

    Let X_i\sim N(\mu,\sigma^2) ; where [i=1,2,\ldots,n] Z_i\sim N(0,1) ; where [i=1,2,\ldots,n] Proof that \frac{(\bar X-\mu)}{\sigma} and \sum_{i=1}^n\frac{(X_i-\bar X)^2}{\sigma^2} are independent, which implies \bar X and \sum_{i=1}^n(X_i-\bar X)^2 are independent. If i show that \bar...