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The University of Sydney School of Mathematics and Statistics NSW 2006 Australia Sydney University Mathematical Society Problem Competition 2009 1. The sisters Alice, Bess, and Cath have become proficient at fa ctorizing numbers, so their father David invents a puzzle for them. He chooses three secret integers a,b,c, all greater than 1, and
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The University of Sydney - maths.usyd.edu.au
www.maths.usyd.edu.auSUMS Problem Competition 2007 Page 3 whose first coordinate x1 is either 0 or 1, while the females are those such that x1 is either α or α +1. To construct the schedule, we index the rounds by the one-dimensional F4-subspaces of Fn 4.
8: The Black-Scholes Model - University of Sydney
www.maths.usyd.edu.auThe Black-Scholes Model M = (B,S) Assumptions of the Black-Scholes market model M = (B,S): There are no arbitrage opportunities in the class of trading strategies. It is possible to borrow or lend any amount of cash at a constant interest rate r ≥ 0. The stock price dynamics are governed by a geometric Brownian motion.
Table of Standard Integrals - University of Sydney
www.maths.usyd.edu.auTable of Standard Integrals 1. Z xn dx= xn+1 n+1 +C (n6= 1) 2. Z dx x = lnjxj+C 3. Z e xdx= e +C 4. Z sinxdx= cosx+C 5. Z cosxdx= sinx+C 6. Z tanxdx= ln cosx +C 7. Z cotxdx= ln sinx
-INVESTIGATIONS ON THE THEORY .OF ,THE BROWNIAN …
www.maths.usyd.edu.au(*) A. Einstein, Ann. d. Phys., 11, p. 170, 1903. MOVEMENT OF SMALL PARTICLES g and 3F RT RT p=-alr*=Y*lCi=Nv* It has been shown by this analysis that the exist- ence of an osmotic pressure can be deduced from the molecular-kinetic theory of Heat ; and that as far as osmotic pressure is concerned, solute
10 Hypothesis Testing with Two Independent Samples
www.maths.usyd.edu.au• the one-sample z-test for population proportion p, based on one sample; ... existing techniques are revised. Advances occur whenever a new technique is proved to be better than the old. Hence we need ... One-sided t-test-2.262 0 1.94 t9 P-value=0.084 a=0.05 (RR) 0.042 0.042
1.Cochran, W.G. (1963) Sampling Techniques Survey …
www.maths.usyd.edu.au4.Systematic sampling and cluster sampling. 5.Sampling with unequal probabilities. Probability proportional to size(PPS) sampling. The Horvitz-Thompson estimator. SydU STAT3014 (2015) Second semester Dr. J. Chan 1. STAT3014/3914 Applied …
A short list of the most useful R commands
www.maths.usyd.edu.auA short list of the most useful R commands A summary of the most important commands with minimal examples. See the relevant part of the guide for better examples.
Data Visualization with ggplot2 : : CHEAT SHEET
www.maths.usyd.edu.auData Visualization with ggplot2 : : CHEAT SHEET ggplot2 is based on the grammar of graphics, the idea that you can build every graph from the same components: a data set, a coordinate system, and geoms—visual marks that represent data points.
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The University of Sydney - maths.usyd.edu.au
www.maths.usyd.edu.auSUMS Problem Competition 2007 Page 3 whose first coordinate x1 is either 0 or 1, while the females are those such that x1 is either α or α +1. To construct the schedule, we index the rounds by the one-dimensional F4-subspaces of Fn 4.
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