variance and expectations? Mean - The mean of a discrete random variable X is a weighted average of the possible values that the random variable can take. Unlike the sample mean of a group of observations‚ which gives each observation equal weight‚ the mean of a random variable weights each outcome xi according to its probability‚ pi. The mean also of a random variable provides the long-run average of the variable‚ or the expected average outcome over many observations.The common symbol for the
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Perhaps because of these two traditional traits and due to the influence of the Mahabharata‚ the Ramayana and the Bhagavad Gita‚ he considers the receipt of defective goods and services as an act of fate or unfavourable planetary position in his horoscope. When a new television or refrigerator purchased by him turns out to be defective from day one‚ he takes it reticently‚ blaming it on his fate or as the consequence of the wrongs committed by him in his previous birth. Very often he is
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factory there is a small chance 1/500 for any pen to be defective. The pens are supplied in packs of 10. Use this probability to calculate the approximate number of packets containing no defective‚ one defective and two defective pens‚ respectively in a consignment of 20‚000 packets [ e^(--0.02) =0.9802 ] Ans. : 19604‚ 392‚ 3.92=4 respectively 2. A manufacturer who produces medicine bottles finds that 0.1% of the bottles are defective. The bottles are packed in the boxes of 500 bottles
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Probability theory Probability: A numerical measure of the chance that an event will occur. Experiment: A process that generates well defined outcomes. Sample space: The set of all experimental outcomes. Sample point: An element of the sample space. A sample point represents an experimental outcome. Tree diagram: A graphical representation that helps in visualizing a multiple step experiment. Classical method: A method of assigning probabilities that is appropriate when all the experimental
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1/08/13 Probability Primer Principles of Econometrics‚ 4th Edition Probability Primer Page 1 ! Announcement: ! Please make sure you know who your tutor is and remember their names. This will save confusion and embarrassment later. ! Kai Du (David) ! Ngoc Thien Anh Pham (Anh) ! Zara Bomi Shroff Principles of Econometrics‚ 4th Edition Probability Primer Page 2 Chapter Contents ¡ P.1 Random Variables ¡ P.2 Probability Distributions ¡ P.3 Joint
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I. Probability Theory * A branch of mathematics concerned with the analysis of random phenomena. The outcome of a random event cannot be determined before it occurs‚ but it may be any one of several possible outcomes. The actual outcome is considered to be determined by chance. * The word probability has several meanings in ordinary conversation. Two of these are particularly important for the development and applications of the mathematical theory of probability. One is the interpretation
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P(S) The symbol for the probability of success P(F) The symbol for the probability of failure p The numerical probability of a success q The numerical probability of a failure P(S) = p and P(F) = 1 - p = q n The number of trials X The number of successes The probability of a success in a binomial experiment can be computed with the following formula. Binomial Probability Formula In a binomial experiment
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Introduction The word Probability derives from probity‚ a measure of the authority of a witness in a legal case in Europe‚ and often correlated with the witness ’s nobility. In a sense‚ this differs much from the modern meaning of probability‚ which‚ in contrast‚ is used as a measure of the weight of empirical evidence‚ and is arrived at from inductive reasoning and statistical inference. A short history of Probability Theory............ The branch of mathematics known as probability theory was inspired
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support recreation and tourism all over the world. At a fundamental level‚ marine life helps determine the very nature of our planet. Marine organisms contribute significantly to the oxygen cycle‚ and are involved in the regulation of the Earth’s climate. Shorelines are in part shaped and protected by marine life‚ and some marine organisms even help create new land. Many species are economically important to humans‚ including Nylon Shells (Phapia undulata). It is also becoming understood that the well-being of marine
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cutting a deck of cards for $1‚000. What is the probability that the card for the gambler will be the following? a. A face card – there are 12 face cards in a deck of 52 cards. The probability would be 12/52 b. A queen – there are 4 queens in a deck‚ so the probability would be 4/52 c. A Spade - There are 13 cards of each suit so the probability is 13/52 or ¼. d. A jack of spades - There is only 1 jack of spades in a deck‚ so the probability would be 1/52 2. The employees in the textile
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