A Course in Mathematical Statistics phần 9 pps

... fertilizers. Comparison of a certain brand of gasoline with and without an additive by using it in several cars. Comparison of different brands of gasoline by using them in several cars. Comparison of the wearing ... distributed, under H. We may summarize all relevant information in a table (Table 1) which is known as an Analysis of Variance Table. EXAMPLE 3 For a numerical exampl...

Ngày tải lên: 23/07/2014, 16:21

... 0 .99 9 98 6 0 .99 9 96 1 0 .99 9 91 0 0 .99 9 816 0 .99 9 657 0 .99 9 406 6 0 .99 9 99 9 0 .99 9 99 7 0 .99 9 99 1 0 .99 9 97 9 0 .99 9 95 7 0 .99 9 91 7 7 1.000 000 1.000 000 0 .99 9 99 9 0 .99 9 99 8 0 .99 9 99 5 0 .99 9 99 0 8 1.000 ... 0 .99 96 0 .99 84 0 .99 47 0 .98 57 18 1.0000 0 .99 99 0 .99 93 0 .99 76 0 .99 28 19 0 .99 97 0 .99 89 0 .99 65 20 1.0000 0 .99 99 0 .99...

Ngày tải lên: 23/07/2014, 16:21

... Determine the minimum sample size n required by using the Binomial tables (if possible) and also by using the CLT. 13.3.10 The number X of fatal traffic accidents in a certain city during a year may ... Testing Hypotheses 13.3.4 The rainfall X at a certain station during a year may be assumed to be a normally distributed r.v. with s.d. σ = 3 inches and unknown mean μ . For the pa...

Ngày tải lên: 23/07/2014, 16:21

... the Intermediate Value Theorem (see, for example, Theorem 3(ii) on page 95 in Calculus and Analytic Geometry, 3rd edition ( 196 6), by George B. Thomas, Addison-Wesley Publishing Company, Inc., Reading, Massachusetts) there ... permutation of the integers 1 through n. From the definition of a determinant and the fact that each row and column contains exactly one 1 and the rest all 0, it f...

Ngày tải lên: 23/07/2014, 16:21

... black at least 2 cards in are red exactly 1 card in is an ace the first card in is a diamond, the second is a heart and the third is a club card in is a diamond, 1 is a heart and 1 is a club 2.4.30 ... which may be quite an abstract set, into a subset of the real line ޒ with which we are already familiar. This is, actually, achieved by the introduction of the concept...

Ngày tải lên: 23/07/2014, 16:21

... confidence intervals for the variance of a normal distribution,” Journal of the American Statistical Association, 195 9, Vol. 54, pp. 674–682) for n = 2(1) 29 and 1 − α = 0 .90 , 0 .95 , 0 .99 , 0 .99 5, 0 .99 9). To ... repeated at will, in many other cases this is, indeed, the case. In the latter case, as a rule, it is advantageous not to fix the sample size in advance, but to keep...

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... () ∈ [] = () ∈ [] By assuming the existence of an MLE, we have that the maximum at the left-hand side above is attained at an MLE ˆ θθ θθ θ. Then, clearly, the right-hand side attains its maximum at ˆ θθ θθ θ*, ... The Case Where Complete Sufficient Statistics Are Not Available or May Not Exist: Cramér–Rao Inequality When complete, sufficient statistics are available, the problem of findi...

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... differentiation as follows: 178 7 Stochastic Independence with Some Applications To start with, consider the probability space (S, A, P) and recall that k events A 1 , , A k are said to be independent ... a function defined on the entire real line and taking values in the complex plane. Those readers who are not well versed in matters related to complex-valued functions may feel un...

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... improper integral in which the limits are taken symmetrically. As an example, for σ = 1, μ = 0, we have, in terms of the principal value integral, I xdx x x AA A A A A A A A * lim lim log lim ... over x, as x varies in G, of such intervals is equal to G. The same is true if we consider only those intervals corresponding to all rationals x in G. These intervals are countably...

Ngày tải lên: 23/07/2014, 16:21

... . n nj j AA →∞ = ∞ = 1 U We recall that AAAA AAA AAA AA j j ccc = ∞ =+ ∩ () +∩∩ () +⋅⋅⋅ =+ − () +− () +⋅⋅⋅ 1 11 2 1 23 121 32 U , by the assumption that A n ↑. Hence P A P A PA PA A PA A PA A PA PA A ... n n nn n nn 23 2 10 21 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ + ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ +⋅⋅⋅+ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ =− ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ − ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ =−− relationships characterizing the independence of A j , j = 1, , n and they...

Ngày tải lên: 23/07/2014, 16:21