tailieunhanh - Handbook of mathematics for engineers and scienteists part 160

Handbook of mathematics for engineers and scienteists part 160. Tài liệu toán học quốc tế để phục vụ cho các bạn tham khảo, tài liệu bằng tiếng anh rất hữu ích cho mọi người. | Chapter 21 Mathematical Statistics . Introduction to Mathematical Statistics . Basic Notions and Problems of Mathematical Statistics . Basic problems of mathematical statistics. The term statistics derives from the Latin word status meaning state. Statistics comprises three major divisions collection of statistical data their statistical analysis and development of mathematical methods for processing and using the statistical data to draw scientific and practical conclusions. It is the last division that is commonly known as mathematical statistics. The original material for a statistical study is a set of results specially gathered for this study or a set of results of specially performed experiments. The following problems arise in this connection. 1. Estimating the unknown probability of a random event 2. Finding the unknown theoretical distribution function The problem is stated as follows. Given the values x1 . xn of a random variable X obtained in n independent trials find at least approximately the unknown distribution function F x of the random variable X. 3. Determining the unknown parameters of the theoretical distribution function The problem is stated as follows. A random variable X has the distribution function F x 01 . Ok depending on k parameters 01 . Ok whose values are unknown. The main goal is to estimate the unknown parameters 01 . Ok using only the results X1 . Xn of observations of the random variable X . Instead of seeking approximate values of the unknown parameters 01 . Ok in the form of functions 0 . Ok in a number of problems it is preferable to seek functions 0 L and 0 R i 1 2 . k depending on the results of observations and known variables and such that with sufficient reliability one can claim that 0 l 0 0 R i 1 2 . k . The fnnpfionQ qtiH Z3 i 1 Q lc ilfp cqIIaH tHp h iiin nripk for Z Z i unctions i l aim j r l i . rv are caned me cofyLCieftce uounuaf les ioi u 1 . Ufa. 4. Testing statistical hypotheses The problem is