SIG Interview Questions 1. Torpedo question: 2 torpedoes‚ each with 1/3 probability of hitting/ sinking a ship 2. I have 20% chance to have cavity gene. If I do have the gene‚ there is 51% chance that I will have at least one cavity over 1 year. If I don’t have the gene‚ there is 19% chance that I will have at least one cavity over 1 year. Given that I have a cavity in 6 months‚ what’s the probability that I have at least a cavity over 1 year? 3. What is the probability of 5 people with different
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investment in fast expanding booming economy. * COVARIANCE The covariance measures the strength of relationship between two numerical random variable X and Y. * A positive covariance indicates positive relationship. * A negative covariance indicates negative relationship. * Expected value is sum of two random variable. E(X+Y) = E(X) + E(Y) E(X) = (0.1)(-300)+(0.2)(-200)+(0.5)(100)+(0.2)(400) = 60 E(Y) = (0.1)(1200)+(0.2)(600)+(0
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between successive breakdowns is 0-6 weeks. Based on the Bigelow Manufacturing example‚ the formula for continuous probability function for the time between breakdowns is f(x) =x/18‚ 0 < x < 6 weeks. To simulate the interval successive breakdowns‚ random numbers were generated and the result multiplied by 6 and Square root. This gives the number of weeks between machine breakdowns. Cumulative Time was also generated adding the result of the generated square root and stopping just a bit above 52 weeks
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corresponding to 3 successes. Find its mean and standard deviation.( Mean=6‚ Sd= Sq. root of 6) 5. A soft-drink vending machine is set so that the amount of drink dispensed is a random variable with a mean of 200 ml. And a standard deviation of 15 ml. Find the probability that the average amount dispensed in a random bottle is at least 204 ml.? (
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Descriptive Statistics: On the Way to Elementary Probability 4.1 Solutions Probability Theories 5.1 Solutions 5.2 Additional problems 5.3 Solutions of additional problems Discrete Random Variables 6.1 Solutions vii 1 1 3 3 7 7 15 15 25 25 29 29 30 31 33 33 v 2 3 4 5 6 vi CONTENTS 7 Continuous Random Variables 7.1 Solutions Dependence‚ Correlation‚ and Conditional Expectation 8.1 Solutions 37 37 43 43 47 49 49 57 58 60 62 65 66 67 69 8 Appendix A R – A software tool for
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The days to repair component was calculated by using the probability distribution of repair times given. This was used along with a set of random numbers based on 100 breakdowns a year. Then‚ a vlookup was used and the probability distribution per day to come up with the days to repair‚ which varies based on the random number that excel generates. The random number represents the probability of how many days it would take to repair the copier. TIME BETWEEN BREAKDOWNS The time between breakdowns
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The Research Foundation of CFA Institute Literature Review Risk Management: A Review Sébastien Lleo‚ CFA Imperial College London The concept of risk has been central to the theory and practice of finance since Markowitz’s influential work nearly 60 years ago. Yet‚ risk management has only emerged as a field of independent study in the past 15 years. Advances in the science of risk measurement have been a main contributor to this remarkable development as new risk measures have been proposed
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Uncertainty in the Movie Industry: Does Star Power Reduce the Terror of the Box O±ce?¤ Arthur De Vany Department of Economics Institute for Mathematical Behavioral Sciences University of California Irvine‚ CA 92697 USA W. David Walls School of Economics and Finance The University of Hong Kong Pokfulam Road Hong Kong Abstract Everyone knows that the movie business is risky. But how risky is it? Do strategies exist that reduce risk? We investigate these questions using a sample of over
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discussion will first briefly overview probability in relation to random events and then present its applications to blackjack. In drawing connections between mathematics‚ more specific to our case‚ probability‚ and blackjack first requires the definition of how random events and probability relate to outcomes of random events. Probability can be defined as the way in which mathematics describes randomness. Something is considered to be random if the individual outcomes of that something are subject to
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customers this Friday. The waitress averages 5 customers that leave no tip on Fridays: λ = 5. Random Variable : The number of customers that leave her no tip this Friday. We are interested in P(X = 7). Ex. 2 During a typical football game‚ a coach can expect 3.2 injuries. Find the probability that the team will have at most 1 injury in this game. A coach can expect 3.2 injuries : λ = 3.2. Random Variable : The number of injuries the team has in this game. We are interested in [pic]. Ex. 3. A
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