Probability via Expectation | Peter Whittle | SpringerA uniform distribution, sometimes also known as a rectangular distribution, is a distribution that has constant probability. The probability density function and cumulative distribution function for a continuous uniform distribution on the interval are. These can be written in terms of the Heaviside step function as. The continuous distribution is implemented as UniformDistribution [ a , b ]. For a continuous uniform distribution, the characteristic function is.
The Expected Value and Variance of Discrete Random Variables
It seems that you're in Germany. We have a dedicated site for Germany. The third edition of constituted a major reworking of the original text, and the preface to that edition still represents my position on the issues that stimulated me first to write. The present edition contains a number of minor modifications and corrections, but its principal innovation is the addition of material on dynamic programming, optimal allocation, option pricing and large deviations. These are substantial topics, but ones into which one can gain an insight with less labour than is generally thought. They all involve the expectation concept in an essential fashion, even the treatment of option pricing, which seems initially to forswear expectation in favour of an arbitrage criterion.
Autor: Peter Whittle 4th ed. Probability via Expectation. Autor: Peter Whittle.
The algebra of random variables provides rules for the symbolic manipulation of random variables , while avoiding delving too deeply into the mathematically sophisticated ideas of probability theory. Its symbolism allows the treatment of sums, products, ratios and general functions of random variables, as well as dealing with operations such as finding the probability distributions and the expectations or expected values , variances and covariances of such combinations. In principle, the elementary algebra of random variables is equivalent to that of conventional non-random or deterministic variables. However, the changes occurring on the probability distribution of a random variable obtained after performing algebraic operations are not straightfoward. Therefore, the behavior of the different operators of the probability distribution, such as expected values, variances, covariances, and moments , may be different from that observed for the random variable using symbolic algebra. It is possible to identify some key rules for each of those operators, resulting in different types of algebra for random variables, apart from the elementary symbolic algebra: Expectation algebra, Variance algebra, Covariance algebra, Moment algebra, etc.