Discrete Probabilistic Models
... When we talk about a random variable, it is helpful to think of an associated random experiment or trial. A random experiment or trial can be thought of as any activity that will result in one and only one of several well-defined outcomes, but one does not know in advance which one will occur. The s ...
... When we talk about a random variable, it is helpful to think of an associated random experiment or trial. A random experiment or trial can be thought of as any activity that will result in one and only one of several well-defined outcomes, but one does not know in advance which one will occur. The s ...
Pdf - Text of NPTEL IIT Video Lectures
... continuous distribution, he may have to wait for 0 to 1 minute. If we see, the total allotment of the probabilities, in this case the probability of 0 less than X less than or equal to 1, is actually equal to 3 by 4. So, probability x equal to 0 and probability of x lying between 0 1 is 3 by 4, so i ...
... continuous distribution, he may have to wait for 0 to 1 minute. If we see, the total allotment of the probabilities, in this case the probability of 0 less than X less than or equal to 1, is actually equal to 3 by 4. So, probability x equal to 0 and probability of x lying between 0 1 is 3 by 4, so i ...
On the Black-Box Complexity of Optimally
... depends on the security parameter, seems counter-intuitive (yet see the comparison below with statistically hiding commitments which do have constructions with the number of rounds depending on the security parameter). In particular, our negative result implies that the use of oblivious transfer (a ...
... depends on the security parameter, seems counter-intuitive (yet see the comparison below with statistically hiding commitments which do have constructions with the number of rounds depending on the security parameter). In particular, our negative result implies that the use of oblivious transfer (a ...
Chapter 2 Random Variables
... 2.7 Two Function of Two Random Variables ........................................................................................ 24 2.7.1 Probability Density Function ( Discrete Random Variables)................................................ 24 2.7.2 Probability Density Function ( Continuous Rand ...
... 2.7 Two Function of Two Random Variables ........................................................................................ 24 2.7.1 Probability Density Function ( Discrete Random Variables)................................................ 24 2.7.2 Probability Density Function ( Continuous Rand ...
probability theory and stochastic processes
... Set: A set is a well defined collection of objects. These objects are called elements or members of the set. Usually uppercase letters are used to denote sets. The set theory was developed by George Cantor in 1845-1918. Today, it is used in almost every branch of mathematics and serves as a fundamen ...
... Set: A set is a well defined collection of objects. These objects are called elements or members of the set. Usually uppercase letters are used to denote sets. The set theory was developed by George Cantor in 1845-1918. Today, it is used in almost every branch of mathematics and serves as a fundamen ...
INTRODUCTION TO PROBABILITY THEORY by Victor
... In Example 1 if A = {ω2 } then A is the event that the child is a boy. In Example 2 if A = {ω1 }, then A is the event that a head appears on the flip of the coin. In Example 3 if A = {ω2 , ω4 , ω6 } then A is the event when appears even face. In Example 4 if A = {ω1 , ω2 , ω3 } then A is the event th ...
... In Example 1 if A = {ω2 } then A is the event that the child is a boy. In Example 2 if A = {ω1 }, then A is the event that a head appears on the flip of the coin. In Example 3 if A = {ω2 , ω4 , ω6 } then A is the event when appears even face. In Example 4 if A = {ω1 , ω2 , ω3 } then A is the event th ...
A Philosopher`s Guide to Probability
... Bishop Butler‘s dictum that ―Probability is the very guide of life‖ is as true today as it was when he wrote it in 1736. It is almost platitudinous to point out the importance of probability in statistics, physics, biology, chemistry, computer science, medicine, law, meteorology, psychology, economi ...
... Bishop Butler‘s dictum that ―Probability is the very guide of life‖ is as true today as it was when he wrote it in 1736. It is almost platitudinous to point out the importance of probability in statistics, physics, biology, chemistry, computer science, medicine, law, meteorology, psychology, economi ...
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.