First the binomial random variable is expressed as a sum of n Bernoulli distributed random variables: X = X1 + ··· + Xn. Then since E(Xi) = p for each Xi, the sum evaluates (by Theorem 4.2.3) to np. Recall that Theorem 4.2.3 says: Theorem 4.2.3 If X1 + ··· + Xn ...
Polytopes associated with lattices of subsets and maximising expectation of random variables The present paper originated from a problem in Financial Mathematics concerned with calculating the value of a European call option based on multiple assets each following the binomial model. The model led to an...
binomial distributionexpectationgeometric distributionindependent random variableslog‐logistic distributionmomentsPoisson pmftransform methodsWeibull distributionThe variable-entered Karnaugh map (VEKM) is shown to be the natural map for representing and manipulating general 'big' Boolean functions that are not ...
We give the proof of a tight lower bound on the probability that a binomial random variable exceeds its expected value. The inequality plays an important role in a variety of contexts, including the analysis of relative deviation bounds in learning theory and generalization bounds for unbounded los...
6.3 6.3 Expectation and variance of a discrete random variable 18:03 Chapter 7 - The binomial and geometric... 7.1 7.1-1 The binomial distribution 29:08 7.2 7.1-2 The binomial distribution 18:12 7.3 7.1.3 Expectation and variance 12:51 ...
Coupon Collectors, q-Binomial Coefficients and the Unsatisfiability Threshold The problem of determining the unsatisfiability threshold for random 3-SAT formulas consists in determining the clause to variable ratio that marks the (experimentally observed) abrupt change from almost surely satisfiable formulas...
6.1 6.1 Discrete random variables 06:39 6.2 6.2 Probability distributions 28:34 6.3 6.3 Expectation and variance of a discrete random variable 18:03 Chapter 7 - The binomial and geometric... 7.1 7.1-1 The binomial distribution 29:08
conditional expectation(条件期望讲义)A Conditional expectation A.1Review of conditional densities,expectations We start with the continuous case.This is sections6.6and6.8in the book.Let X,Y be continuous random variables.We defined the conditional density of X given Y to be f X,Y(x,y)f ...
Noun1.binomial distribution- a theoretical distribution of the number of successes in a finite set of independent trials with a constant probability of success Bernoulli distribution distribution,statistical distribution- (statistics) an arrangement of values of a variable showing their observed or theoreti...
He covers the basic financial instruments; fundamental principles of financial modeling and arbitrage valuation of derivatives; the concept of conditional expectation, the discrete time binomial model and its application to stochastic finance; the most important results from the theory of martingales in th...