Lec10 CONTINUOUS RANDOM VARIABLES
... This refers to the number of values X can take on, not the size of the values. The random variable is continuous if the range of X is uncountably infinite and X has a suitable pdf (see below). Typically an uncountably infinite range results from an X that makes a physical measurement—e.g., the posit ...
... This refers to the number of values X can take on, not the size of the values. The random variable is continuous if the range of X is uncountably infinite and X has a suitable pdf (see below). Typically an uncountably infinite range results from an X that makes a physical measurement—e.g., the posit ...
6.16 independent and dependent practice
... Example- There are 6 beads in a bag, 3 are red, 2 are yellow and 1 is blue. What is the probability of picking a yellow and without replacing it, next choosing a red?? ...
... Example- There are 6 beads in a bag, 3 are red, 2 are yellow and 1 is blue. What is the probability of picking a yellow and without replacing it, next choosing a red?? ...
Discrete Fourier Transform
... In fact all physical processes do obey to a causality principle in time, namely the future of a system can depend on its past, but not viceversa. (*) On the contrary when t is a 1-D coordinate in space, the value of { u(t,)} at any two points t1,t2 can have a perfectly symmetric relation. /(*)Note ...
... In fact all physical processes do obey to a causality principle in time, namely the future of a system can depend on its past, but not viceversa. (*) On the contrary when t is a 1-D coordinate in space, the value of { u(t,)} at any two points t1,t2 can have a perfectly symmetric relation. /(*)Note ...
Random Systems
... Fortunately, random (or stochastic) systems can be as simple to understand as deterministic systems, if we’re careful to ask the right questions. It’s a mistake to try to guess the value of the toss of a fair coin, because it is completely uncertain. But we can quite precisely answer questions about ...
... Fortunately, random (or stochastic) systems can be as simple to understand as deterministic systems, if we’re careful to ask the right questions. It’s a mistake to try to guess the value of the toss of a fair coin, because it is completely uncertain. But we can quite precisely answer questions about ...
COMP245: Probability and Statistics 2016
... Q2) Suppose two events E and F are mutually exclusive. State the precise conditions under which they may also be independent. ...
... Q2) Suppose two events E and F are mutually exclusive. State the precise conditions under which they may also be independent. ...
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.