Pnk =n! / (n-k)! Daca trebuie sa alegem din n k si NU conteaza ordinea. How many possibilities? Cnk = n! / ((n-k)!* k!) Relative Frequency = Frequency of A/ Total Frequency = P(A). While statistics (proportions-population) - past events, Probability (sample) - future events. 1) A U B, A or B P(A or B) = P(A) + P(B) - P(A and B) Mutually exclusive => P(A and B)=0 2) P(B/A) Independent=P(B). Dependent=P(B/A)= P(A and B)/ P(A) 3) Intersection A ∩ B ///Dependent :P(A and B) = P(A) x P(B|A) Independent
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at least 4 correct to pass II: 5 questions, each question has 4 choices, must answer at least 3 correct to pass III: 4 questions, each question has 6 choices, must answer at least 2 correct to pass Which final exam format offers the highest probability to pass? a. Final exam I b. Final exam II c. Final exam III d.
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discrete probability distribution. X P(X) 2 .50 8 .30 10 .20 Mean 2*.50+8*.30+10*.20 = 5.4 Variance 2^2*.50+8^2*.30+10^2*.20-5.40^2 = 2.00+19.20+20.00-29.16 = 12.04 2a. The total number of ways to choose 3 members out of 8 is C(8, 3) = 8!/(3! 5!) = (8*7*6*5*4*3*2*1) / ((3*2*1) * (5*4*3*2*1)) = 56. The total number of ways to choose 3 tenured people from 6 is C(6,3) = 6!/(3! 3!) = (6*5*4*3*2*1) / ((3*2*1) * (3*2*1)) = 20. So the probability is 20/56
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Risk and Return “Believe me! The secret of reaping the greatest fruitfulness and the greatest enjoyment from life is to live dangerously!” —Friedrich Wilhelm Nietzsche Are You the “Go-for-It” Type? The financial crisis has people buzzing about “systematic risk.” This term means different things in different contexts. Traditionally, systematic risk has referred to the non-diversifiable risk that comes from the impact the overall market has on individual investments. This risk is also known
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Hermalin Consulting “The Nerd in the Know” TM To: Mr. William Jaeger From: Benjamin E. Hermalin, ph.d. Re: Harvesting Decision I have analyzed your harvesting decision problem. Figure 1 represents your problem in terms of a decision tree. Botrytis [.4] 2 storm [.5] 4 wait 5 no storm 3 [.5] sell as bulk $12,000 + C $42,000 good luck [.4] okay luck [.4] bad luck [.2] $36,000 [.6] no Botrytis 1 bottle $24,000 - R $67,200 $30,000 $34,200 harvest now Figure 1: The harvesting decision represented
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Question 1 First year students marks of Managerial Statistics Marks – Managerial examinations 2010 Percentage Achieved | No of students | 0 >20 | 5 | 20 > 40 | 18 | 40 > 60 | 30 | 60 >80 | 20 | 80 > 100 | 4 | Total | 77 | 1 (a) Chart 1: Histogram of the Managerial Statistics marks obtained (b) Percentage Achieved | No of students | Less Cumulative | More cumulative | 0 >20 | 5 | 5 | 77 | 20 > 40 | 18 | 235 | 72 | 40 > 60 | 30 | 53 | 54 |
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Mendelian Genetics in Drosophila Melanogaster: Fruit Fly Inheritance Results Total count for section & course data: Cross | Phenotype | Section 6 Total | Course Total | ap/ap x +/+ | wt | 211 | 2604 | | Apterous | 58 | 824 | | | | | | | | | X(w)X(w) x X(+)Y | wt females | 15 | 707 | | white females | 9 | 597 | | wt males | 13 | 633 | | White males | 13 | 614 | Totals | 760 | 11,754 | Table 1: Total counts for section and course data. Four crosses were
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equally weighted portfolio of 10 assets, calculate the amount of unsystematic and systematic risk in her portfolio. 2. (Diversification over time). Suppose an investor invests $100 in a stock that in each period can either double or half with equal probability. The returns in each period are uncorrelated. (a) Calculate the variance of the investors’ dollar position after one period. (b) Calculate the variance of the investor’s dollar position after holding the stock for two periods. Report the ratio of
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Interval data: Real numbers, i.e. heights, weights, prices Box plot -Values are real numbers Outliers: -All calculations are valid less than 25th Percentile-Data may be treated as ordinal or nominal 1.5*interquatile Ordinal Data: order poor = 1, fair = 2, good = 3, very good = 4 or -Values must represent the ranked order of the data. Larger than 75th -Calculations based on an ordering process are valid. Percentile+1.5*interquatile -Data may be treated as nominal but not as interval. Nominal Data:
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DRA Assignment 2 – Recreational Properties 1) FRAMING THE DECISION 1.a) Decisions a) He can exercise the option and buy the land. In this case, the possible decisions are: a.1) Sell the land without any development a.2) Develop the land with a development cost of £ 5 million and the sell it for a higher profit b) He can avoid to exercise the option and invest in another investment that will give to him a certain profit. c) Try to negotiate an option extension in order to be able to delay his
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