reliability (probability of working). Assume components fail independently. What is the probability that the entire system works? (only write down the expression) P(works) = P(A)*P(B) + P(C)*P(D)*P(E) – P(A)*P(B)*P(C)*P(D)*P(E) = 0.7*0.7 + 0.8*0.8*0.8 – 0.7*0.7*0.8*0.8*0.8 2. Finish the following Bayes theorem (only the basic version‚ not with total probability rule): For two events A and B‚ with P(A) > 0 and P(B) > 0‚ P(A|B) = P(B|A) * P(A) / P(B) 3. The probability that a regularly
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Application of Probability in daily life Introduction This study is based on the paper “In all probability‚ Probability is not all” written by Danny Helman (2004). This paper is about how much probability theory can be applied in a popular game of lottery. It is believed that since the lottery is a game of chance‚ no strategy can be of any use. Burger (1991) says that the lottery is a situation where no control is possible. It is a situation where outcomes are chance determined. The paper investigates
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study‚ the probability of cases being appealed and reversed in the three different courts are: a. For the total cases disposed in the Common Pleas Court there is a 0.1129 probability of a case being appealed and reversed. b. For the total cases disposed in the Domestic Relations Court there is a 0.1604 probability of a case being appealed and reversed. c. For the total cases disposed in the Municipal Court there is a 0.2080 probability of a case being appealed and reversed. 2. The probability of a case
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the z-score for which the area under the standard normal curve to its left is 0.04 9) Determine the two z-scores that divide the area under the standard normal curve into a middle 0.874 area and two outside 0.063 areas. Find the indicated probability or percentage for the normally distributed variable. 10) The variable X is normally distributed. The mean is μ = 15.2 and the standard deviation is σ = 0.9.
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concentrates primarily on the acceptance and communication aspects. Keywords: Risk management‚ risk analysis‚ risk acceptance‚ risk communication 1. Introduction To an engineer‚ the “risk” associated with a hazard is a combination of the probability that that hazard will occur and the consequences of that hazard. Consequences to be considered include injury or loss of life‚ reconstruction costs‚ loss of economic activity‚ environmental losses‚ etc. In all cases‚ the safety issue has to be addressed
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Model 2-door 4-door Automatic 135 351 Manual 251 213 If a car is picked at random from the fleet‚ calculate the probability that it is: (i) automatic‚ (2 marks) (ii) automatic or 2-door‚ (2 marks) (iii) manual and 4-door‚ (2 marks) (iv) 2-door given that it is manual transmission. (2 marks) 4. Consider a random variable M with the probabilities specified in the following figure: k 3 6 9 12 15 P (M = k) (i) Find E (M). (2 marks) (ii)
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BSP2014 STOCHASTIC Tri 2’ 2012/2013 Mid-Term Exam Question 1 a) A continuous random variable X has the probability density function given by 3 2 ; 0 x2 (2 x) f ( x) 8 0 ; otherwise (i) Calculate the mean of X and variance of X. (ii) Calculate . (iii) Find . b) Given X ~ Exp ( 2) and the moment generating function (MGF) of X is given M X (t ) 2 2t . Find the mean and variance of X. c) Given for x = 1‚ 2‚ 3‚ 4. Find the moment generating
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information is incomplete. To deal with this realm of inductive logic‚ usage of probability theory becomes essential. As per the new perceptions‚ probability theory today is recognized as a valid principle of logic that is used for drawing inferences related to hypothesis of interest. E.T. Jaynes in the late 20th century‚ shared the view of “Probability theory as logic”. Today this is commonly called Bayesian probability theory in recognition with the work done in the late 18th century by an English
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formal definitions: Definition 1. A stochastic process is a sequence of events in which the outcome at any stage depends on some probability. Definition 2. A Markov process is a stochastic process with the following properties: (a.) The number of possible outcomes or states is finite. (b.) The outcome at any stage depends only on the outcome of the previous stage. (c.) The probabilities are constant over time. If x0 is a vector which represents the initial state of a system‚ then
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Solutions Due before the start of class‚ Wednesday January 16. 1. In Cook County‚ each day is either sunny or cloudy. If a day is sunny‚ the following day will be sunny with probability 0.60. If a day is cloudy‚ the following day will be cloudy with probability 0.70. Suppose it is cloudy on Monday. a) What is the probability that it will be sunny on Wednesday? There are two mutually exclusive ways that it could end up being sunny on Wednesday. P(Sunny Wednesday) = P(Sunny Tuesday AND Sunny Wednesday)
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