Chapter 7 Random Processes - RIT Center for Imaging Science
... The domain of e is the set of outcomes of the experiment. We assume that a probability distribution is known for this set. The domain of t is a set, T , of real numbers. If T is the real axis then X(t, e) is a continuous-time random process, and if T is the set of integers then X(t, e) is a discrete ...
... The domain of e is the set of outcomes of the experiment. We assume that a probability distribution is known for this set. The domain of t is a set, T , of real numbers. If T is the real axis then X(t, e) is a continuous-time random process, and if T is the set of integers then X(t, e) is a discrete ...
13. A psychologist determined that the number of sessions required
... each type of computer? b. What is the variance of the number of computers per household for each type of computer? c. Make some comparisons between the number of laptops and the number of desktops owned by the Journal’s subscribers. 23. a. Laptop: E (x) = .47(0) + .45(1) + .06(2) + .02(3) = .63 Desk ...
... each type of computer? b. What is the variance of the number of computers per household for each type of computer? c. Make some comparisons between the number of laptops and the number of desktops owned by the Journal’s subscribers. 23. a. Laptop: E (x) = .47(0) + .45(1) + .06(2) + .02(3) = .63 Desk ...
Lecture 4
... VIII. The Coefficient of Variation A measure of relative dispersion is the square root of the variance, divided by the mean, and hence it is unit-less. For the binomial , this coefficient is: Coefficient of Variation = n p (1 – p) n p = (1/n)((1 – p)/p). For a fair coin this would be 1/n .So ...
... VIII. The Coefficient of Variation A measure of relative dispersion is the square root of the variance, divided by the mean, and hence it is unit-less. For the binomial , this coefficient is: Coefficient of Variation = n p (1 – p) n p = (1/n)((1 – p)/p). For a fair coin this would be 1/n .So ...
Creating a Probability Model
... Goal: The goal of this activity is for students to grasp the understanding of how to put together a probability model for the rolling of a single die and also the sum of the rolls of two dice. Materials: This worksheet and a pencil. Optional: two pairs of dice Directions: Have students get into grou ...
... Goal: The goal of this activity is for students to grasp the understanding of how to put together a probability model for the rolling of a single die and also the sum of the rolls of two dice. Materials: This worksheet and a pencil. Optional: two pairs of dice Directions: Have students get into grou ...
1 Gambler`s Ruin Problem
... fortune of $N , without first getting ruined (running out of money). If the gambler succeeds, then the gambler is said to win the game. In any case, the gambler stops playing after winning or getting ruined, whichever happens first. There is nothing special about starting with $1, more generally the ...
... fortune of $N , without first getting ruined (running out of money). If the gambler succeeds, then the gambler is said to win the game. In any case, the gambler stops playing after winning or getting ruined, whichever happens first. There is nothing special about starting with $1, more generally the ...
Randomness
Randomness is the lack of pattern or predictability in events. A random sequence of events, symbols or steps has no order and does not follow an intelligible pattern or combination. Individual random events are by definition unpredictable, but in many cases the frequency of different outcomes over a large number of events (or ""trials"") is predictable. For example, when throwing two dice, the outcome of any particular roll is unpredictable, but a sum of 7 will occur twice as often as 4. In this view, randomness is a measure of uncertainty of an outcome, rather than haphazardness, and applies to concepts of chance, probability, and information entropy.The fields of mathematics, probability, and statistics use formal definitions of randomness. In statistics, a random variable is an assignment of a numerical value to each possible outcome of an event space. This association facilitates the identification and the calculation of probabilities of the events. Random variables can appear in random sequences. A random process is a sequence of random variables whose outcomes do not follow a deterministic pattern, but follow an evolution described by probability distributions. These and other constructs are extremely useful in probability theory and the various applications of randomness.Randomness is most often used in statistics to signify well-defined statistical properties. Monte Carlo methods, which rely on random input (such as from random number generators or pseudorandom number generators), are important techniques in science, as, for instance, in computational science. By analogy, quasi-Monte Carlo methods use quasirandom number generators.Random selection is a method of selecting items (often called units) from a population where the probability of choosing a specific item is the proportion of those items in the population. For example, with a bowl containing just 10 red marbles and 90 blue marbles, a random selection mechanism would choose a red marble with probability 1/10. Note that a random selection mechanism that selected 10 marbles from this bowl would not necessarily result in 1 red and 9 blue. In situations where a population consists of items that are distinguishable, a random selection mechanism requires equal probabilities for any item to be chosen. That is, if the selection process is such that each member of a population, of say research subjects, has the same probability of being chosen then we can say the selection process is random.