'Conditional expectation' presentation slideshows

The probabilistic method & infinite probability spaces

The probabilistic method & infinite probability spaces. Events and Random Variables. An event is a subset of sample space S. A random variable is a (real-valued) function on S. Eg: we throw a black and a white ball into 2 equally likely bins. event E = {both balls fall in same bin}

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Probability III: The Probabilistic Method

Probability III: The Probabilistic Method. Recap. Random Variables. An event is a subset of S. A Random Variable (RV) is a (real-valued) function on S. Example : Event A : the first die came up 1. Random Variable X : the value of the first die. E.g., X(<3,5>)=3, X(<1,6>)=1.

685 views • 60 slides

Pattern Recognition and Machine Learning

Pattern Recognition and Machine Learning. Chapter 1: Introduction. Example. Handwritten Digit Recognition. Polynomial Curve Fitting . Sum-of-Squares Error Function. 0 th Order Polynomial. 1 st Order Polynomial. 3 rd Order Polynomial. 9 th Order Polynomial. Over-fitting.

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Random Vectors

662 views • 51 slides

Probability III: The probabilistic method & infinite probability spaces

Probability III: The probabilistic method & infinite probability spaces. Recap. Random Variables. An event is a subset of S. A Random Variable (RV) is a (real-valued) function on S. Example : Event A : the first die came up 1. Random Variable X : the value of the first die.

648 views • 49 slides

Returns and Expected Returns

Returns and Expected Returns. 1. Holding period return P t = Price of asset at time t R t = % return from time t-1 to t CF t = cash flow from time t-1 to t - e.g. dividend R 1 = = (%capital gain) + (%dividend yield)

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5.1. Jointly Distributed Random Variables

Chapter 5 Joint Probability Distributions and Random Samples. 5.1. Jointly Distributed Random Variables. Joint Probability Mass Function.

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Smart Monte Carlo: Various Tricks Using Malliavin Calculus Quantitative Finance, NY, Nov 2002 Eric Benhamou eric.benhamo

Smart Monte Carlo: Various Tricks Using Malliavin Calculus Quantitative Finance, NY, Nov 2002 Eric Benhamou eric.benhamou@gs.com Goldman Sachs International. Agenda. Motivation for Fast Monte Carlo Engines Smart Computation of the Greeks Typology of Options and Practical Use

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Randomized Algorithms CS648

Randomized Algorithms CS648. Lecture 25 Derandomization using conditional expectation A probability gem. Derandomization using conditional expectation. Problem 1 : Large cut in a graph. Problem: Let be an undirected graph on vertices and edges. Compute a cut of size at least .

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Affymetrix Latin Square Experiment

Affymetrix Latin Square Experiment. One lot of 14 arrays were used for the study using spikes along with the background-- enriched RNA from DR153 (Ecoli) strain.

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chapter three

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CSE 780: Design and Analysis of Algorithms

CSE 780: Design and Analysis of Algorithms. Lecture 7: Prob. Analysis Randomized Alg. Expected Complexity. Probabilistic method: Given a distribution for all possible inputs Derive expected time based on distribution Randomized algorithm: Add randomness in the algorithm

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Nonparametric estimation of conditional VaR and expected shortfall

Nonparametric estimation of conditional VaR and expected shortfall. Outline. Introduction Nonparametric Estimators Statistical Properties Application. Introduction.

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Partition and Condition = Divide and Conquer

Partition and Condition = Divide and Conquer. Tutorial 8, STAT1301 Fall 2010, 16NOV2010, MB103@HKU By Joseph Dong. Recall: A Partition on a Set. Any exhaustive and disjoint collection of subsets of a given set forms a partition of that set. E.g.

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Simulating Exchangeable Multivariate Archimedean Copulas and its Applications

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ENEE 324: Conditional Expectation

ENEE 324: Conditional Expectation. Richard J. La Fall 2004. Conditional Expectation. Example: Toss a coin 3 times X = number of heads in 3 independent tosses Y = length of the longest run of heads Compute. 1/8. 3. 1/4. 2. 3/8. 1/8. 1. 1/8. 3. Conditional Expectation.

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Omitted Variable Bias

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More about Posterior Distributions

More about Posterior Distributions. The process of Bayesian inference involves passing from a prior distribution to a posterior distribution. It is natural to expect that some general relations might hold between these two distributions.

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Stat 35b: Introduction to Probability with Applications to Poker

Stat 35b: Introduction to Probability with Applications to Poker Outline for the day, Tue 3 /13/ 12: Collect Hw4. 2011 WSOP main event. Review list. Answers to hw4. Project B tournament. More examples. Final Exam: Tuesday, March 20, 11:30 AM - 2:30 PM, here in Royce 156.

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Conditional Probability & Conditional Expectation

Conditional Probability & Conditional Expectation. Conditional distributions Computing expectations by conditioning Computing probabilities by conditioning. Discrete conditional distributions. Given a joint probability mass function the conditional pmf of X given that Y = y is

1.26k views • 6 slides