The Optimized Confidence Of The Ratio Of The Two Normal Random Variables

In the traditional systerm field of probability and statistics, when all of the four parameters are unknown, the confidence interval of the the ratio of the two normal random variables has the form as follow:( S₁² and s₂² are the sample variances, n₁ and n₂ are the sample capacitiesand (1 - α) is the confidence degree)Here the pdf of the F distribution is asymmetric, the confidence interval above is not the shortest under the equal confidence degree, so it is not the best in this sense.Considering the problem above ,this paper analysised the confidence and obtained the optimized one and proved its existence and uniqueness . Forethermore we displayed its advantages conpairing it to the results counted by traditional method.The result of this paper is that the new method enriched the application fields of the knowledge and developed a more accurate way.