such as all numbers greater than 0 (including numbers whose decimals continue indefinitely, such as pi = 3.14159265...). Overall, the concepts of discrete and continuous probability distributions and the random variables they describe are the underpinnings...
Closed form expressions are derived for the probability of a demand pattern being satisfied, in both, discrete and continuous time. Known reliability measures are identified as special cases. We illustrate the theory on two examples: the first is a system comprising three power transmission lines, ...
Probability Distribution of a Random Variable A random variable is the possible outcome(s) of a random probabilistic event. Continuous random variables are presented with a continuous function and they can take infinitely many different values within the given interval. Some examples are arrival times...
ExamplesNumber of heads in 10 coin flips, number of students in a class, number of stars in a galaxyHeight, weight, temperature, time, volume, speed, distance, pressure, energy, voltage Probability distributionRepresented by adiscrete probability distributionRepresented by acontinuous probab...
While randomness defines both discrete andcontinuous variables, their values are not entirely unpredictable. The probability of each value is well-defined and quantifiable using probability functions. By understanding the properties of these probability functions, you can make predictions and draw conclusions...
Cat has a master's degree in education and is currently working on her Ph.D.Cite this lesson Data refers to statistics and other types of information collected for research and analysis. Data comes in various types, including discrete and continuous. Explore the definition and examples of data...
Thus far, most of the previous results assumed that all the variables are either discrete or continuous. We propose to compute a new Bayesian score for each subset of discrete and continuous variables, and to obtain a structure that maximizes the posterior probability given examples. We evaluate ...
Powerful modern math library for PHP: Features descriptive statistics and regressions; Continuous and discrete probability distributions; Linear algebra with matrices and vectors, Numerical analysis; special mathematical functions; Algebra License MIT license 2.4k stars 242 forks Branches Tags Activity ...
Let f be a continuous mapping from X onto Y. Then f is a perfect mapping if and only if the product f× iz of f with the identity mapping on Z is a closed mapping for every space Z. (Hint: To prove the ‘if’ part, assume f−1(q) is not compact; then it has a non-con...
So, in our case, the notion of controllability and reachability are equivalent. Most of the criteria on controllability in the continuous-time case also hold in the discrete-time case. Here we will state and prove only one criterion analogous to (ii) of Theorem 6.2.1....