Practice problems using various statistical methods If n independent random variables X have normal distributions with means μ and the standard deviations σ , then determine the distribution of a. I....

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Practice problems using various statistical methods

If n independent random variables X have normal distributions with means μ and the standard deviations σ , then determine the

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Answer 1

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T Distribution arises when estimating the mean of a normally distributed population in situations where the sample size is small and population standard deviation is unknown. E(X)=0 ,VAR(X)=n/n-2, df=n

F Distribution arises frequently as the null distribution of a test statistic, most notably in the analysis of variance.E(X)=n/n-2

m,n is the degrees of freedom

$2n(mn - 2) varX = n(m-2)2(m-4)$ \

chi squared is one of the most widely used probability distributions in inferential statistics, notably in hypothesis testing or in construction of confidence intervals. E(X)=n, V(X)=2n, n is the degrees of freedom

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