What is a random sample? - Random sampling is a group of subjects randomly selected from a larger group (population) randomly without a bias and influence by the information you are interested in. 2. Why does randomly selecting a number between one and zero help in creating a random sample from a cdf? - A cumulative density function range from zero to one. By selecting a number between zero and one will help create your random sample. Zero to one is the population and if I pick random number like:
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}P{C is in service | C arrives at x, and x = (0,t] } Since theorem of Poisson Process, The theorem is that Given that N(t) =n, the n arrival times S1, S2, …Sn have the same distribution as the order statistics corresponding to n independent random variables uniformly distributed on the interval (0, t) Thus, P{C is in service | C arrives between time (0, t] } Since let y=t-x, x=0 → y=t, x=t →y=o, dy=-dx Therefore, In conclusion, ------ (1) 1-a Solution
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QAT1 Task 5 Revised Task A. Develop New Product 1.) Develop Thoroughly= $210,200 2.) Develop Rapidly= $55,700 Consolidate Existing Product 3.) Strengthen Products= $64,900 4.) Reap Without Investing= $6,400 Task B. The decision alternative is to develop new products thoroughly, or decision alternative 1, with the expected value (EV) of $210, 200. 1. Decision alternative 1 has the highest expected value ($210,200) of all four branches, thus making it the most favorable decision. To
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Dear Ms. Lopez: Based on a quantitative and qualitative assessment of the current offer, it is my recommendation NOT to accept the offer of $22,500,000 for Uptown Plaza because there is an approximate 80% probability that the present value of Uptown Plaza will be greater than the current offer if you wait until the lease renewals for the tenants in question are in place (see Appendix A). The below assessment summarizes the downside, but more importantly in this case, upside risk of waiting to
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Advanced Financial Models Example sheet 1 - Michaelmas 2010 Michael Tehranchi Problem 1. In a one-period model, a num´raire asset is called risk-free if its time-1 price e i i is not random: if asset i is risk-free, then S1 = (1 + ri )S0 for a real constant ri > −1, called the risk-free rate of return. Suppose that a market model has at least one risk-free asset. Show that if there is no arbitrage, then the risk-free rate of return is unique, in the sense that if both asset i and asset
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1. Number of days needed to repair the copier. Machine Probability of Cumulative Random number repair time repair time P(y) probability range, r2 1 0.2 0.2 0.00 - 0.20 2 0.45 0.65 0.21- 0.65 3 0.25 0.9 0.66 - 0.90 4 0.1 1 0.91 - 1 2. Intervals between successive breakdowns: The probability distribution of the random variable varies between the times of 0 to 6 weeks, with the probability increasing as time goes on. This can be approximated by the function F(x) = x/18, for 0”x”6, where
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ˆ The criterion which is commonly used in judging the performance of an estimator or predictor y of a random variable y is its mean-square error defined ˆ 2 by E{(y − y ) }. If all of the available information on y is summarised in its ˆ marginal distribution, then the minimum-mean-square-error prediction is simply the expected value E(y). However, if y is statistically related to another random variable x whose value can be observed, and if the form of the joint distribution of x and y is known,
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Assumptions of Portfolio Theory • Investors are rational. • Investors are basically risk averse. • Investors wants to maximize the returns from his/her investments for a given level of risk. • Investor portfolio includes all of his/her assets and liabilities. • The relationship between the returns of assets in the portfolio is important since the returns from these investments interact with each other. Risk Aversion • Portfolio Theory assumes investors are basically risk averse. • Risk aversion
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1. The Hurwicz criterion is a compromise between the maximax and maximin criteria. The Hurwicz criterion is the weighted sum of the maximax and maximin. So, the answer is true. 2. The minimin criterion is optimistic. The minimin criterion is NOT applied to the profit payoff table. It is applied to the cost table. In this situation we want to minimize cost as much as possible. So, if we can do it this is optimistic criterion. 3. A business owner is trying to decide whether to buy, rent
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BUSINESS RESEARCH METHODS PROJECT ON GALLUP INTRODUCTION Gallup, Inc. is a research-based, global performance-management consulting company. Founded by George Gallup in 1935, the company became famous for its public opinion polls, which were conducted in the United States and other countries. Gallup works with major businesses and organizations around the world. In 1988, four
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