mathematics - introduction to probability theory

... X Y y {Y y} ≤ Y=2X+1 x=(y-1)/2 {X (y-1)/2} ≤ X Y y {Y y} ≤ Y=X 2 y -y ½ ½ F (x) X x µ σ 0 1 2 3 4 5 6 7 8 9 10 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 x Fx(x) Rayleigh

Ngày tải lên: 08/04/2014, 12:21

... Chapter 1 Introduction to Probability Theory 1.1 The Binomial Asset Pricing Model The binomial asset pricing model provides a powerful tool to understand arbitrage pricing theory and probability theory. ... removed in the Cantor set construction of Example 3.2.  CHAPTER 1. Introduction to Probability Theory 35 In addition to tossing a coin, another common random expe...

Ngày tải lên: 18/10/2013, 03:20

... F 1 ⊗F 2 , 1 × 2 ) is called product probability space. An introduction to probability theory Christel Geiss and Stefan Geiss February 19, 2004 20 CHAPTER 1. PROBABILITY SPACES One can prove that (F 1 ⊗ ... 1.2.2. Interpretation: Coin-tossing with one coin, such that one has head with probability p and tail with probability 1 − p. Then µ n,p ({k}) is equals the probability, t...

Ngày tải lên: 31/03/2014, 16:23

... X Y y {Y y} ≤ Y=2X+1 x=(y-1)/2 {X (y-1)/2} ≤ X Y y {Y y} ≤ Y=X 2 y -y ½ ½ F (x) X x µ σ 0 1 2 3 4 5 6 7 8 9 10 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 x Fx(x) Rayleigh

Ngày tải lên: 08/04/2014, 12:21

... distribution is unlimited.  NONRESIDENT TRAINING COURSE  December 1988 Mathematics, Pre-Calculus and Introduction to Probability NAVEDTRA 14141 

Ngày tải lên: 31/03/2014, 16:24

Ngày tải lên: 17/12/2013, 15:19

... z)=x 2 + z 2 (6) which is illustrated in Figure xxx. 15 -2 -1 .75 -1 .5 -1 .25 -1 -0 .75 -0 .5 -0 .25 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 -2 -1 .25 -0 .5 0.25 1 1.75 0 1 2 3 4 5 6 7 8 y x z y = x^2 + z^2 Figure ... 2001 1 Introduction to Portfolio Theory Consider the following investment problem. We can invest in two non-dividend paying stocks A and B over...

Ngày tải lên: 17/12/2013, 15:21

... corresponds to exactly one of the outcomes of the random variable ¯ X, so it is natural to assign probability 1/8 to each of these. We assign probability 0 to the other 16 outcomes. In each case, the probability ... up heads with probability p, and tails with probability q. Now suppose that this coin is tossed twice. Using a frequency interpretation of probability, it is re...

Ngày tải lên: 20/12/2013, 19:15

Ngày tải lên: 01/01/2014, 17:43

... the interview, the candidate is lost to her. She wants to de- cide on a strategy for deciding when to stop and accept a candidate that will maximize the probability of getting the best candidate. ... particles, such as photons and protons. It turns out that experiments have shown that certain types of elementary particles exhibit behavior 14 W. Feller, Introduction to Probability...

Ngày tải lên: 21/02/2014, 09:20