analysis is an important component of engineering work that draws on the areas of probability and statistics. As the name suggests‚ reliability analysis is concerned with the investigation of the failure rates of components and systems‚ which are typically represented as probabilities. Life testing is a general term used to describe the experimentation and statistical analysis performed to investigate failure rates. Probability distributions that are used to model failure times are typically the exponential
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that the sun will die one day- it may even be tomorrow. We have no exact knowledge of the sun; all that we know is through predictions of science based on previous data. Keeping this in mind‚ we cannot assume that the probability of it rising tomorrow is greater than the probability of anything else‚ say gravity overcoming it and turning it into a black hole‚ therefore it is with no certainty that I can say that the sun will rise tomorrow. Without a complete and conclusive knowledge of all the possibilities
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MATH 107 NAME:_______________________ EXAM 2 Show all work for credit and keep answers exact when possible. 1. Classify the following statement as an example of classical‚ empirical‚ or subjective probability and explain your reasoning. According to your doctor he feels the chance of you surviving a surgery is 0.85. Subjective; based upon his feelings. 2. Determine the two events described in the study. Do the results indicate that the events are independent or dependant?
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to represent the population (Burns & Grove 2001:365; Polit & Beck 2006:259). These are two types of sampling‚ namely probability and non-probability sampling (Burns & Grove 2001:374‚ Polit & Beck 2006:260). In this study both probability and non-probability sampling was used. The location was selected using probability sampling and the respondents were selected using non-probability
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line. Erlang (a Danish Telephone engineer) began a study of congestion and waiting times in the completion of telephone calls. Operating Characteristic (performance Measure) for a waiting Line Model Probability that no units are in the system Probability that an arriving unit has to wait for service Average Number of units in waiting line or system Average Time a unit spends in waiting line or system Make a decision that balance desirable service level against the
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A goes to the first teller‚ B to the second teller‚ and C queues. To standardize the answers‚ let us assume that TA is the length of time in minutes starting from noon until Customer A departs‚ and similarly define TB and TC . (a) What is the probability that Customer A will still be in service at time 12:05? (b) What is the expected length of time that A is in the system? (c) What is the expected length of time that A is in the system if A is still in the system at 12:05? (d) How likely is
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are: 1 2 probability sampling methods non-probability sampling methods PROBABILITY SAMPLING In probability sampling (random-based sampling) every member of the target population has a chance of being selected for the sample. Sampling units are selected from the target population on a random basis. There are four probability-based sampling methods: 1 2 3 4 simple random sampling systematic random sampling stratified random sampling cluster random sampling. PROBABILITY SAMPLING
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MDM4U – Grade 12 Data Management – Exam Unit 1: One Variable Analysis Types of Data Numerical Data Discrete: consists of whole numbers Ie. Number of trucks. Continuous: measured using real numbers Ie‚ Measuring temperature. Categorical Data: cannot be qualitatively measured Nominal: Data which any order presented makes sense Ie‚ Eye Colour‚ Hair Colour. Ordinal Data: better if sorted or ordered Ie‚ Date and Time‚ scalar options Collecting Data Primary: collected by yourself Secondary:
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Decision Trees DECISION MAKING WITHOUT PROBABILITIES Optimistic Approach Conservative Approach Minimax Regret Approach DECISION MAKING WITH PROBABILITIES Expected Value of Perfect Information RISK ANALYSIS AND SENSITIVITY ANALYSIS Risk Analysis Sensitivity Analysis DECISION ANALYSIS WITH SAMPLE INFORMATION An Influence Diagram A Decision Tree Decision Strategy Risk Profile Expected Value of Sample Information Efficiency of Sample Information COMPUTING BRANCH PROBABILITIES 4.2 4.3 4.4 4.5 4.6
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Mathematical Modelling 2 Week 3: Discrete Random Variables Stephen Bush Department of Mathematical Sciences MM2: Statistics - Week 3 - 1 Random Variables • Reference: Devore § 3.1 – 3.5 • Definitions: • An experiment is any process of obtaining one outcome where the outcome is uncertain. • A random variable is a numerical variable whose value can change from one replicate of the experiment to another. • Sample means and sample standard deviations are random variables • They
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