Gdtyjr

There are some mathematical formulas in the table that don't automatic line break, resulting in poor display and Overfull warning. So, how to fix it?

Here is the latex minimal working example:

documentclassarticle

% support for `multirow` command
usepackagemultirow

begindocument

Let $ (X_1, X_2, ldots, X_n_1) $ denote a random sample of size $ n_1 $ from a distribution that is $ X sim N(mu_1, sigma_1^2) $, $ (Y_1, Y_2, ldots, Y_n_2) $ denote a random sample of size $ n_2 $ from a distribution that is $ Y sim N(mu_2, sigma_2^2) $, respectively. $ overlineX $, $ S_1^2 $, $ overlineY $, $ S_2^2 $ is the corresponding sample mean and sample variance, and
[
S_ omega^2 = frac(n_1 - 1) S_1^2 + (n_2 - 1) S_2^2n_1 + n_2 - 2
]

Note that two random samples are independent, and $ overlineX $, $ S_1^2 $, $ overlineY $, $ S_2^2 $ are unknown parameters.

The following table lists the interval estimator of $ mu_1 - mu_2 $ and $ sigma_1^2 / sigma_2^2 $ with $ 1 - alpha $ confidence interval.

begintable[ht]
captionInterval estimator for difference of means and ratio of variance in two normal populations
centering

begintabularc
hline
multicolumn2cunknown parameter & $ 1 - alpha $ confidence interval tabularnewline
hline
multirow2*$ mu_1 - mu_2 $ & $ sigma_1^2 $, $ sigma_2^2 $ known & $ left( overlineX - overlineY - U_fracalpha2 sqrtfracsigma_1^2n_1 + fracsigma_2^2n_2, overlineX - overlineY + U_fracalpha2 sqrtfracsigma_1^2n_1 + fracsigma_2^2n_2 right) $ tabularnewline
cline2-3
 & $ sigma_1^2 $, $ sigma_2^2 $ unknown, but $ sigma_1^2 = sigma_2^2 $ & $ left( overlineX - overlineY - T_fracalpha2 (n_1 + n_2 - 2) S_omega sqrtfrac1n_1 + frac1n_2, overlineX - overlineY + T_fracalpha2 (n_1 + n_2 - 2) S_omega sqrtfrac1n_1 + frac1n_2 right) $ tabularnewline
hline
multicolumn2c$ sigma_1^2 / sigma_2^2 $ & $ left( fracS_1^2 / S_2^2F_alpha / 2 (n_1 - 1, n_2 - 1), fracS_1^2 / S_2^2F_1- alpha / 2 (n_1 - 1, n_2 - 1) right) $ tabularnewline
hline
endtabular
endtable

enddocument