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Importance and Application of probability:
Importance of probability theory is in all those areas where event are not certain to take place as same as starting with games of chances. Probability has become one of the basis tools of statistics. Statistics and probability are much interrelated with each other that it is difficult to discuss statistics without understanding the meaning of probability. A knowledge of probability theory makes it easier, simpler and possible to interpret the statistical result, as many of the statistical procedures include involve conclusions based on samples which are randomly choosen.
Probability theory is being applied not only in mathematical problems but also for the solutions of social economical, political and business problems. The insurance insustry emerged in the 19th century, required exact or definite knowledge about the risk of loss inorder to calculate premium. Within few decades the concept of probability has assumed great importance and the mathematical theory of probability has become the basis of statistical application and social and decision making. In fact probability has become a part of everyone life. In personal and management decisions one faces uncertainty and uses probability theory. By organising information and considering it systematically, one will be able to recognise his or her assumptions, communicate his or reasoning to others and make a better decision than he or she could by using a shot in the dark approach. Probability theory in fact is the foundation of statistical conclusion or inference.
Systematic Random Sampling This method is generally used in such cases where a complete list of the population is available from which sample has to be selected. Under this
In simple regression the dependent variable Y was assumed to be linearly related to a single variable X. In real life, however, we often find that a dependent variable may depend o
Estimate the standard deviation of the process: Draw the X (bar) and R charts for the data given and give your comments about the process under study. Estimate the standard de
If the economy does well, the investor's wealth is 2 and if the economy does poorly the investor's wealth is 1. Both outcomes are equally likely. The investor is offered to invest
Theories of Business forecasting
Q. Find the inverse Laplace transform of Y (s) = s-4/s 2 + 4s + 13 +3s+5/s 2 - 2s -3. Q. Use the Laplace transform to solve the initial value problem y''+ y = cos(3t), y(0) =
Perform clustering of the unlabeled data set. You could use provided initial centroids set or generate your own. Also there could be considered next stopping criteria : - maxim
This box plot displays the diversity wfood; the data ranges from 0.05710 being the minimum value and 0.78900 being the maximum value. The box plot is slightly positively skewed at
The Maju Supermarket stocks Munchies Cereal. Demand for Munchies is 4,000 boxes per year and the super market is open throughout the year. Each box costs $4 and it costs the store
Show that the ISB in a bin containing the origin of the double exponen-tial density, f(x) = exp(-|x|)/2, is O(h 3 ); hence, the discontinuity in the derivative of f does not have a
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