“概率、统计”考点分析与试题解析

“概率与统计”以近半个学期的学习内容进入了高中课本，占整个高中数学新增内容的30％。2004年将有85％以上的省市参加新课程高考。本文以近几年上海、全国新课程卷和各地模拟试题为依据，谈谈自己的看法，供同行参考，并请赐教。

A Novel Statistical Delay Model Based on the Birnbaum-Saunders Distribution for RLC Interconnects in 90nm Technologies

For performance optimization such as placement,interconnect synthesis,and routing, an efficient and accurate interconnect delay metric is critical,even in design tools development like design for yield （DFY） and design for manufacture （DFM）. In the nanometer regime, the recently proposed delay models for RLC interconnects based on statistical probability density function （PDF）interpretation such as PRIMO,H-gamma,WED and RLD bridge the gap between accuracy and efficiency. However, these models always require table look-up when operating. In this paper, a novel delay model based on the Birnbaum-Saunders distribution （BSD） is presented. BSD can accomplish interconnect delay estimation fast and accurately without table look-up operations. Furthermore, it only needs the first two moments to match. Experimental results in 90nm technology show that BSD is robust, easy to implement,efficient,and accurate.

DAMAGE DETECTION FOR COMPOSITE STRUCTURE UNDER TEMPERATURE CHANGES USING LAMB WAVES

A two-step method is proposed for detection and identification of invisible impact damage in composite structure under temperature changes using Lamb waves.First,a statistical outlier analysis is employed to distinguish whether the changes of Lamb wave signals are induced by damage within a monitoring area or are only affected by temperature changes.Damage indices are defined after the Lamb wave signals are processed by Fourier transform,and a Monte Carlo procedure is used to obtain the damage threshold value for the damage indices at the undamaged state.If the damage indices in the operation state exceed the threshold value,the presence of damage is determined.Then,a probabilistic damage imaging algorithm displaying probabilities of the presence of damage within the monitoring area is adopted to fuse information collected from multiple actuator-sensor paths to identify the location of damage.Damage indices under damaged state are used to generate the diagnostic image.Experimental study on a stiffened composite panel with random temperature changes is performed to demonstrate the effectiveness of the proposed method.

On Kendall's Conjecture for an Extended Birth-death Q-processes with Instantaneous State and Catastrophes

A new structure with the special property that instantaneous state and catas-trophes is imposed to ordinary birth-death processes is considered. Kendall's conjecture forthe processes is proved to be right.

A Feedback Scheme for Fountain Codes Based Transport Protocol in Space Communications

This paper proposed a practical- feedback scheme for fountain codes based transportprotocol in space communications. In the proposed scheme, the sender is signaled by two types of acknowledgment （ACK） packets.Before decoding, packet loss probability isestimated on the receiver side and encapsulated intoa soft ACKand sent to the sender.After decoding,decoding results are encapsulated into hard ACKsandsent to the sender. There are two contributionsin the proposed scheme： 1. Empl layer calculation instead layer statistics to estimate oying physical of application the packet loss probability of space channel, which can improvethe accuracy and practicality. 2. A cascade overhead-failure probability relationship between the sender and the receiver has been analyzed to help determine the exact numberof packetsneeded byfountain decoding.Simulations show that for space communications,compared with the existing space transport protocols, fountain codes based transport protoeolwith the proposed schemecan not only ensure transmission reliability, but also greatly improvelink utilization.

Assessing impact of oil spills in fairways in Chinese Bohai Sea with the impact matrix method

The density of traffic in Bohai Sea of China is growing,so the evaluation of the impact of potential oil spills becomes necessary.However,the impact of potential oil spills at a large temporal-spatial scale has seldom been studied.In this paper,the effects of potential oil spills in seven main fairways in Chinese Bohai Sea and the risks of five environmental sensitive areas(ESAs)being polluted are studied.A three-dimensional hydrodynamic model,coupled with Lagrangian particle tracking model,was constructed to simulate the transportation of oil spills.Hypothetical oil particles with an idealized,passive tracer were released along fairways and their transportation over20-day and180-day periods were simulated,respectively.An environmental impact matrix was built to reveal the relationship between oil spills in fairways and the pollution of ESAs.Results showed that in short term,Z4and Z5had high risk of being polluted by oil spills.Oil particles released along Fairways1,2and7had strong pollution effects.In long term,Z1,Z3,Z4and Z5had medium risk of being polluted.Oil particles released along Fairway3had strong pollution effects.This study might provide useful data to support marine environment protection.

Probabilistic Top-k Query:Model and Application on Web Traffic Analysis

Top-k ranking of websites according to traffic volume is important for Internet Service Providers(ISPs) to understand network status and optimize network resources. However, the ranking result always has a big deviation with actual rank for the existence of unknown web traffic, which cannot be identified accurately under current techniques. In this paper, we introduce a novel method to approximate the actual rank. This method associates unknown web traffic with websites according to statistical probabilities. Then, we construct a probabilistic top-k query model to rank websites. We conduct several experiments by using real HTTP traffic traces collected from a commercial ISP covering an entire city in northern China. Experimental results show that the proposed techniques can reduce the deviation existing between the ground truth and the ranking results vastly. In addition, we find that the websites providing video service have higher ratio of unknown IP as well as higher ratio of unknown traffic than the websites providing text web page service. Specifically, we find that the top-3 video websites have more than 90% of unknown web traffic. All these findings are helpful for ISPs understanding network status and deploying Content Distributed Network(CDN).

Traffic Modeling and Probabilistic Process Abstraction

State-based models provide an attractive and simple approach to performance modeling. Unfortunately,this approach gives rise to two fundamental problems: 1) capturing the input loads to a system efficiently within such presentations; and 2) coping with the explosion in the number of states whtn system is compositionally presented. Both problems can be regarded as searching for some optimal representative state model with a minimal const. In this paper a probabilistic feedback search approach (popularly referred to as a genetic algorithm) was presented for locating good models with low (state) cost.

Application of whole body diffusion weighted imaging in bone metastasis

Objective： We evaluated （Whole-Body Diffusion Weighted Imaging, WB-DWl） application in bone metastasis. Methods： WB-DWI with GE 1.5T MR/I was performed on 10 healthy volunteers and 35 patients. WB-DWl and ECT was performed in all 35 patients. Using WB-DWl for detecting bone metastasis and compared them with that of ECT. Results： Background was suppressed in WB-DWl, fat, muscle, vessels and liver appeared same as background. Skeleton showed medium or slightly lower signal. Lymph nodes, some glandular organs, kidneys displayed medium signal. Spleen, testicle, brain tissue were low signal. Bladder, gallbladder were depicted as low signal because of ＂T2 through＂. Bone metastasis were multitude and inequality of size, punctiform, nodosity, column low intensity. Concordance between WB-DWI and ECT was seen in 4 cases. WB-DWl displayed 1 bone metastasis on skull, 46 on rib and sternum, 3 on scapula, 4 on extremities, 83 on vertebral, 36 on pelvic bone. ECT showed 2 bone metastasis on skull, 62 on rib and sternum, 7 on scapula, 9 on extremities, 64 on vertebral, 19 on pelvic bone. WB-DWl was 74% for bone metastasis on rib and sternum, ECT was 77%, 53% for vertebral and pelvic bone. All of the focus were statistics analyses, P 〈 0.05. Total probability distribution inequality if metastasis on different positions. Conclusion： WB-DWI was an effective imaging technology for screening bone metastasis.

New model for deducing directional extrema based on multivariate extremum statistical theory

The parameters of principal and directional extrema in a marine environment are important in marine engineering design, especially for appropriate construction of oceanic platforms and other structures. When designing wave walls and break water structures, the orientation of the breakwater or seawall depends mainly on the direction of the strongest waves. However, the strength of the breakwater and the elevation of the seawall depend on the magnitude of the biggest wave height of the strongest waves. Thus, identification of directional extrema plays an important role in the design of wave factors. When calculating the directional extremum, different materials may require different specific computational methods, yet few theoretical studies have been conducted in this field of research. Based on multivariate extremnm statistical theory, this paper utilizes a discrete random variable to build a joint probability model compounded by a discrete random variable and a multivariate continuous random variable. Furthermore, this paper provides the first investigation on the theories and methodologies to deduce wave directional extrema. The results provide tools for both creating the calculation method of the directional extremum value and providing the rational directional extremum parameters for marine engineering design.

Variability and correlation analysis of physical and mechanical indexes of loess in western Liaoning

Based on the method of probability and statistics, the authors analyzed the physical and mechanical properties of loess in specified area, and discussed its main indexes, the coefficient of variation, and the corre- lation among the physical and mechanical indexes. Regression equations are built among those indexes, the re- suits show that the variability of mechanical indexes is higher than that of the physical indexes, and the physical indexes have better correlation than the relation between physical and mechanical indexes. The conclusions of this study would contribute to further research about loess in western Liaoning.

Research on the Applications of Advanced Mathematics on Mathematical Modeling and the Inner Connections with Linear Algebra and Probability Statistics

In this paper, we conduct research on the applications of advanced mathematics on the mathematical modeling and the inner connections with linear algebra and the probability statistics. Aiming at model in mathematical modeling and solving and model of evaluation and promotion of the two links, put forward the ＂bystander＂ and ＂the authorities＂ this two characters, and points out that excellent mathematical modeling participants should have ＂from a bystander to the authorities＂ and ＂from the authorities to return to bystanders＂ two-way role transformation ability. Great situation in mathematics teaching, by means of the mathematical modeling formed in the development of the teachers, as well as the teaching thought, teaching experience and achievements, the onward march of mathematical experiment should be faster than mathematical modeling. Our research provides the new paradigm for the math development which will be meaningful.

Hypothesis testing analysis and unknown parameter estimation of GPS signal detection

Hypothesis testing analysis and unknown parameter estimation of both the intermediate frequency(IF) and baseband GPS signal detection are given by using the generalized likelihood ratio test(GLRT) approach,applying the model of GPS signal in white Gaussian noise,It is proved that the test statistic follows central or noncentral F distribution,It is also pointed out that the test statistic is nearly identical to central or noncentral chi-squared distribution because the processing samples are large enough to be considered as infinite in GPS acquisition problem.It is also proved that the probability of false alarm,the probability of detection and the threshold are affected largely when the hypothesis testing refers to the full pseudorandom noise(PRN) code phase and Doppler frequency search space cells instead of each individual cell.The performance of the test statistic is also given with combining the noncoherent integration.

Effect of wave spectrum width on the probability density distribution of wind-wave heights

The probability distribution of wave heights under the assumption of narrowband linear wave theory follows the Rayleigh distribution and the statistical relationships between some characteristic wave heights, derived from this distribution, are widely used for the treatment of realistic wind waves. However, the bandwidth of wave frequency influences the probability distribution of wave heights. In this paper, a wave-spectrum-width parameter B was introduced into the JONSWAP spectrum. This facilitated the construction of a wind-wave spectrum and the reconstruction of wind-wave time series for various growth stages, based on which the probability density distributions of the wind-wave heights were studied statistically. The distribution curves deviated slightly from the theoretical Rayleigh distribution with increasing B. The probability that a wave height exceeded a certain value was clearly smaller than the theoretical value for B≥0.3, and the difference between them increased with the threshold value. The relation between the Hs/σ ratio and B was investigated statistically, which revealed that the Hs/σ ratio deviated from 4.005 and declined with B. When B reached 0.698 1, the Hs/σ ratio was 3.825, which is about 95.5% of its original value. This indicates an overestimation in the a potential method for improving the accuracy of the Hs extremely large waves under severe sea states. prediction of Hs from Hs=4.005σ, and provides remote sensing retrieval algorithm, critical for

Georgian Social Insurance Fund Management Problems and Probabilistic and Statistical Analysis of Fund Capital Management

A mathematical model of management of a social insurance fund with exponential insurance reimburse and financing determined social programs is represented and analyzed; A probability density function and fund＇s functioning probabilistic characteristics are obtained, that makes it possible to determine the sufficiency of fund capital at all levels of its management. With the help of conclusion it is possible for particular period of time determine in insurance fund change of cash flow movement speed, on what basis in determined from state tax revenues assigns acceptance necessity and capacity.

Spectrum Allocation for Cognitive Radio Networks with Non-Deterministic Bandwidth of Spectrum Hole

The spectrum allocation for cognitive radio networks(CRNs) has received considerable studies under the assumption that the bandwidth of spectrum holes is static. However, in practice, the bandwidth of spectrum holes is time-varied due to primary user/secondary user(PU/SU) activity and mobility, which result in non-determinacy. This paper studies the spectrum allocation for CRNs with non-deterministic bandwidth of spectrum holes. We present a novel probability density function(PDF) through order statistics as well as its simplified form to describe the statistical properties of spectrum holes, with which a statistical spectrum allocation model based on stochastic multiple knapsack problem(MKP) is formulated for spectrum allocation with non-deterministic bandwidth of spectrum holes. To reduce the computational complexity, we transform this stochastic programming problem into a constant MKP through exploiting the properties of cumulative distribution function(CDF), which can be solved via MTHG algorithm by using auxiliary variables. Simulation results illustrate that the proposed statistical spectrum allocation algorithm can achieve better performance compared with the existing algorithms when the bandwidth of spectrum holes is time-varied.

Probabilistic Loss Differentiation for IEEE 802.11 Wireless Networks

We start this paper by answering the questions： What requirements should a good Loss Differentiation Mechanism （LD） for 802.11 networks in loT meet？ Do the existing LDs work well in 802.11 networks when moving towards loT？ Then we present the four properties that a LD used in loT should own and the two-folded factors that we should consider when designing such a LD. Thereby, a novel LD is proposed utilizing the back- off frozen event to reveal collision probability. Our mechanism works efficiently with standard 802.11 ; only practical statistics information is needed. In ad- dition, our mechanism can be done solely by the sender without introducing extra signaling overhead. Extensive simulations show that our mechanism can be applicable to different scenarios in 802. 11 WLANs.

Probability and Statistical Error of Soil Sampling on Patches Assimilated during Delineation of Precision Farming Management Zones

When precision fanning management zones （MZs） are delineated in an agricultural field for precision nutrient management, unsupervised classification and cluster analysis procedures using remote sensing image analysis software are performed. These unsupervised classification and cluster analysis procedures are performed on the basis of the assumption that grouping of data points into naturally occurring clusters reduces within zone variability. The problem is that, there are small patches of different soil types within each management zone that are regarded as insignificant by the farmer, and are assimilated within larger MZs. These will consequently make soils within a management zone to be inhomogeneous. The objective of this study was to determine the probability of soil sampling occurrences on patches assimilated during delineation of MZs after a cluster analysis was performed. The study was conducted on a 5.0 ha （25°05′34.46″ S and 28°18′30.01″ E） and a 24.4 ha （23°59′04.61″ S and 28°52′29.43″ E） fields in the Waterberg District of the Limpopo Province in South Africa. A bare-soil high resolution Quickbird satellite imagery of a conventionally tilled agricultural field was used to develop MZs in the field. Soils were sampled using systematic unaligned sampling on a 35.0 m and 30.0 m grids for the 24.4 ha and 5.0 ha fields, respectively. Probabilities were calculated based on percentage area assimilated during the cluster analysis procedure that was performed using remote sensing image analysis software. The results indicated that in the 24.4 ha field there were 2.5 ha patches of high and medium zones that were assimilated within the low zone, and thus making low zones non-homogeneous. After cluster analysis and assimilation of patches, the low zone in the 24.4 ha field increased by 45.5% （2.5 ha） while the high zone was 16.4% （2.4 ha） smaller in size. In the smaller field of 5.0 ha, the high zone, which was originally 3.20 ha, lost 0.37 ha （11.6%）, which was assimilated in either low or medium zone. The study indicates that unequal probability proportional to size sampling could be used to minimize error when sampling across precision farming MZs because typically the low, medium and high MZs are not of equal size and do not contribute equally towards the mean values of soil samples.

Statistical Superposition of Crosstalk Effects in Cable Bundles

This paper deals with the analytical derivation of phasor-domain statistical properties of crosstalk in random wire cables due to the superposition of several sources of electromagnetic interference.In this study,statistical characterization of crosstalk in cable bundles,which is available in literature for the case of one source of interference,is extended to the case of several sources operating simultaneously.The superposition of crosstalk effects is analysed in statistical terms,also taking into account the correlation between crosstalk contributions.A further random contribution,which is included in the proposed statistical model,is given by the phase relationship between the sources of interference.Analytical approximate expressions for the crosstalk mean value,variance,and probability density function are derived as functions of the cable bundle features and sources.

Markov Chain Model for Smoking Cessation Treatment

Probabilistic models are commonly used in computational medicine for diagnostics. Smoking cessation is an important issue of modern medicine. According to statistics about third part of male in global population are smokers. It is important to develop new approaches for smoking cessation treatment including methods of early diagnosis and development of individual treatment programs for each patient according to his or her physical peculiarities. One of the promising methods is computerized approach for tobacco treatment including electronic survey and computer data analysis. In this work we propose a probabilistic model based on Markov chain for estimation of patient behavior in the process on medical survey. This analysis can help to find out patient＇s individual characteristics and develop effective personal treatment program. Based on probabilistic model software was developed with aim to enhance diagnosis and developing individual smoking cessation treatment programs for each patient.