Ad
related to: random variable probability definition chemistry example problemsstudy.com has been visited by 100K+ users in the past month
Search results
Results From The WOW.Com Content Network
A random variable is a measurable function: from a sample space as a set of possible outcomes to a measurable space.The technical axiomatic definition requires the sample space to be a sample space of a probability triple (,,) (see the measure-theoretic definition).
Probability density function (pdf) or probability density: function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would equal that sample.
A stochastic process is defined as a collection of random variables defined on a common probability space (,,), where is a sample space, is a -algebra, and is a probability measure; and the random variables, indexed by some set , all take values in the same mathematical space , which must be measurable with respect to some -algebra .
A binomial distributed random variable Y with parameters n and p is obtained as the sum of n independent and identically Bernoulli-distributed random variables X 1, X 2, ..., X n [4] Example: A coin is tossed three times. Find the probability of getting exactly two heads. This problem can be solved by looking at the sample space.
Stochastic (/ s t ə ˈ k æ s t ɪ k /; from Ancient Greek στόχος (stókhos) 'aim, guess') [1] is the property of being well-described by a random probability distribution. [1] Stochasticity and randomness are technically distinct concepts: the former refers to a modeling approach, while the latter describes phenomena; in everyday ...
However, it is possible to define a conditional probability for some zero-probability events, for example by using a σ-algebra of such events (such as those arising from a continuous random variable). [34] For example, in a bag of 2 red balls and 2 blue balls (4 balls in total), the probability of taking a red ball is /; however, when taking a ...
Individual random events are, by definition, unpredictable, but if there is a known probability distribution, the frequency of different outcomes over repeated events (or "trials") is predictable. [ note 1 ] For example, when throwing two dice , the outcome of any particular roll is unpredictable, but a sum of 7 will tend to occur twice as ...
The probability is sometimes written to distinguish it from other functions and measure P to avoid having to define "P is a probability" and () is short for ({: ()}), where is the event space, is a random variable that is a function of (i.e., it depends upon ), and is some outcome of interest within the domain specified by (say, a particular ...