2021년 2월 17일 (수) 07:58에 Pythagoras0님의 편집

2021-02-17T07:58:28Z

Pythagoras0: /* 메타데이터 */ 새 문단

2020-12-26T12:12:40Z

메타데이터: 새 문단

Pythagoras0: /* 노트 */ 새 문단

2020-12-21T14:53:05Z

노트: 새 문단

새 문서

== 노트 ==

===위키데이터===
* ID : [https://www.wikidata.org/wiki/Q176623 Q176623]
===말뭉치===
# A random variable is a variable whose value is unknown or a function that assigns values to each of an experiment's outcomes.<ref name="ref_24d9f8dc">[https://www.investopedia.com/terms/r/random-variable.asp Random Variable]</ref>
# A random variable has a probability distribution that represents the likelihood that any of the possible values would occur.<ref name="ref_24d9f8dc" />
# Let’s say that the random variable, Z, is the number on the top face of a die when it is rolled once.<ref name="ref_24d9f8dc" />
# If random variable, Y, is the number of heads we get from tossing two coins, then Y could be 0, 1, or 2.<ref name="ref_24d9f8dc" />
# Since a random variable can take on different values, it is commonly labeled with a letter (e.g., variable “X”).<ref name="ref_5948d05e">[https://corporatefinanceinstitute.com/resources/knowledge/other/random-variable/ Definition, Types, and Role in Finance]</ref>
# A discrete random variable is a (random) variable whose values take only a finite number of values.<ref name="ref_5948d05e" />
# Each outcome of a discrete random variable contains a certain probability.<ref name="ref_5948d05e" />
# When these are finite (e.g., the number of heads in a three-coin toss), the random variable is called discrete and the probabilities of the outcomes sum to 1.<ref name="ref_1df2804d">[https://www.britannica.com/topic/random-variable Random variable | statistics]</ref>
# A random variable that may assume only a finite...<ref name="ref_1df2804d" />
# The probability distribution for a random variable describes how the probabilities are distributed over the values of the random variable.<ref name="ref_0428c826">[https://www.britannica.com/science/statistics/Random-variables-and-probability-distributions Statistics - Random variables and probability distributions]</ref>
# For a discrete random variable, x, the probability distribution is defined by a probability mass function, denoted by f(x).<ref name="ref_0428c826" />
# This function provides the probability for each value of the random variable.<ref name="ref_0428c826" />
# A continuous random variable may assume any value in an interval on the real number line or in a collection of intervals.<ref name="ref_0428c826" />
# This graph shows how random variable is a function from all possible outcomes to real values.<ref name="ref_982b2b66">[https://en.wikipedia.org/wiki/Random_variable Random variable]</ref>
# As a function, a random variable is required to be measurable, which allows for probabilities to be assigned to sets of its potential values.<ref name="ref_982b2b66" />
# The domain of a random variable is called a sample space.<ref name="ref_982b2b66" />
# A random variable has a probability distribution, which specifies the probability of Borel subsets of its range.<ref name="ref_982b2b66" />
# The probability distribution of a discrete random variable is a list of probabilities associated with each of its possible values.<ref name="ref_539c3c81">[http://www.stat.yale.edu/Courses/1997-98/101/ranvar.htm Random Variables]</ref>
# A continuous random variable is not defined at specific values.<ref name="ref_539c3c81" />
# Suppose a random variable X may take all values over an interval of real numbers.<ref name="ref_539c3c81" />
# In correspondence with general definition of a vector we shall call a vector random variable or a random vector any ordered set of scalar random variables.<ref name="ref_80ac85b4">[https://www.sciencedirect.com/topics/engineering/random-variable-xi Random Variable ξ - an overview]</ref>
# A random variable is a statistical function that maps the outcomes of a random experiment to numerical values.<ref name="ref_7e65357f">[https://www.wolframalpha.com/examples/mathematics/statistics/random-variables/ Alpha Examples: Random Variables]</ref>
# What I want to discuss a little bit in this video is the idea of a random variable.<ref name="ref_1b1c373f">[https://www.khanacademy.org/math/statistics-probability/random-variables-stats-library/random-variables-discrete/v/random-variables Random variables (video)]</ref>
# This is actually a fairly typical way of defining a random variable, especially for a coin flip.<ref name="ref_1b1c373f" />
# We can define another random variable capital Y as equal to, let's say, the sum of rolls of let's say 7 dice.<ref name="ref_1b1c373f" />
# and we are defining a random variable in that way.<ref name="ref_1b1c373f" />
# X Here X is a random variable: every time we select a new bead the outcome changes randomly.<ref name="ref_0f69329c">[https://rafalab.github.io/dsbook/random-variables.html Introduction to Data Science]</ref>
# We are going to define a random variable \(S\) that will represent the casino’s total winnings.<ref name="ref_0f69329c" />
# The probability distribution of a random variable tells us the probability of the observed value falling at any given interval.<ref name="ref_0f69329c" />
# a)\), then we will be able to answer any question related to the probability of events defined by our random variable \(S\), including the event \(S<0\).<ref name="ref_0f69329c" />
# These ideas are unified in the concept of a random variable which is a numerical summary of random outcomes.<ref name="ref_12a230ba">[https://www.econometrics-with-r.org/2-1-random-variables-and-probability-distributions.html Introduction to Econometrics with R]</ref>
# The probability distribution of a discrete random variable is the list of all possible values of the variable and their probabilities which sum to \(1\).<ref name="ref_12a230ba" />
# The cumulative probability distribution function gives the probability that the random variable is less than or equal to a particular value.<ref name="ref_12a230ba" />
# The probability distribution of a discrete random variable is nothing but a list of all possible outcomes that can occur and their respective probabilities.<ref name="ref_12a230ba" />
# A discrete random variable may be defined for the random experiment of flipping a coin.<ref name="ref_3c24a8cd">[https://www.sciencedirect.com/topics/mathematics/discrete-random-variable Discrete Random Variable - an overview]</ref>
# A random variable, Y, could be defined to be the number of times tails occurs in n trials.<ref name="ref_3c24a8cd" />
# It turns out that the probability mass function for this random variable is P Y ( k ) = ( n k ) ( 1 2 ) n , k = 0 , 1 , … , n .<ref name="ref_3c24a8cd" />
# The random variable Z will represent the number of times until the first occurrence of a heads.<ref name="ref_3c24a8cd" />
# A density curve describes the probability distribution of a continuous random variable, and the probability of a range of events is found by taking the area under the curve.<ref name="ref_fe4e5436">[https://courses.lumenlearning.com/boundless-statistics/chapter/discrete-random-variables/ Discrete Random Variables]</ref>
# The mathematical function describing the possible values of a random variable and their associated probabilities is known as a probability distribution.<ref name="ref_fe4e5436" />
# Their probability distribution is given by a probability mass function which directly maps each value of the random variable to a probability.<ref name="ref_fe4e5436" />
# As a result, the random variable has an uncountable infinite number of possible values, all of which have probability 0, though ranges of such values can have nonzero probability.<ref name="ref_fe4e5436" />
# One such example was the term "random quantity", introduced by the outstanding Russian mathematician Chebyshev.<ref name="ref_9fd65f98">[https://nrich.maths.org/13852 What Is a Random Variable, Really?]</ref>
# Once we have a probability space, we can define a random variable on it.<ref name="ref_9fd65f98" />
# if it is a tail"; the probability space (or experiment) itself does not tell us what random variable to use, though some may be more natural than others.<ref name="ref_9fd65f98" />
# Note, therefore, that a random variable is neither random nor a variable: it is just any function we care to choose.<ref name="ref_9fd65f98" />
# In essence, a random variable is a real-valued function that assigns a numerical value to each possible outcome of the random experiment.<ref name="ref_26afb8ea">[https://www.probabilitycourse.com/chapter3/3_1_1_random_variables.php Random Experiments]</ref>
# We'll begin our exploration of the distributions of functions of random variables, by focusing on simple functions of one random variable.<ref name="ref_d795a504">[https://online.stat.psu.edu/stat414/lesson/22 Lesson 22: Functions of One Random Variable]</ref>
# Then, once we have that mastered, we'll learn how to modify the change-of-variable technique to find the probability of a random variable that is derived from a two-to-one function.<ref name="ref_d795a504" />
# The equivalent quantity for a continuous random variable, not surprisingly, involves an integral rather than a sum.<ref name="ref_aa1e144a">[https://amsi.org.au/ESA_Senior_Years/SeniorTopic4/4e/4e_2content_4.html Mean and variance of a continuous random variable]</ref>
# Recall that mean is a measure of 'central location' of a random variable.<ref name="ref_aa1e144a" />
# Guess the probability that the corresponding random variable lies between the limits of the shaded region.<ref name="ref_aa1e144a" />
# The module Discrete probability distributions gives formulas for the mean and variance of a linear transformation of a discrete random variable.<ref name="ref_aa1e144a" />
# We’ll first discuss the probability distribution of a discrete random variable, ways to display it, and how to use it in order to find probabilities of interest.<ref name="ref_589947ca">[https://bolt.mph.ufl.edu/6050-6052/unit-3b/discrete-random-variables/ Discrete Random Variables]</ref>
# We’ll then move on to talk about the mean and standard deviation of a discrete random variable, which are measures of the center and spread of its distribution.<ref name="ref_589947ca" />
# Recall our first example, when we introduced the idea of a random variable.<ref name="ref_589947ca" />
# What is the probability distribution of X, where the random variable X is the number of tails appearing in two tosses of a fair coin?<ref name="ref_589947ca" />
# A random variable—unlike a normal variable—does not have a specific value, but rather a range of values and a density that gives different probabilities of obtaining values for each subset.<ref name="ref_c059e17e">[https://reference.wolfram.com/language/guide/RandomVariables.html Random Variables—Wolfram Language Documentation]</ref>
# The Wolfram Language uses symbolic distributions to represent a random variable.<ref name="ref_c059e17e" />
# A random variable is often introduced to students as a value that is created by some random process.<ref name="ref_cf39ce73">[https://apcentral.collegeboard.org/courses/ap-statistics/classroom-resources/random-variables-vs-algebraic-variables AP Statistics: Random Variables vs. Algebraic Variables]</ref>
# Give students roll dice, flip coins, or draw cards so you can get the idea of a random variable across.<ref name="ref_cf39ce73" />
# However, you need to get students to see that the term “random variable” is used in both a more abstract way and a more varied way in most statistics textbooks.<ref name="ref_cf39ce73" />
# This point value, call it X , is a random variable because its value is determined by the outcome of a random process.<ref name="ref_cf39ce73" />
# A Random Variable in Slide2, is any model input parameter that you have selected and defined a statistical distribution for, using the options in the Statistics menu.<ref name="ref_c94e4d69">[https://www.rocscience.com/help/slide2/slide_model/probability/Random_Variables.htm Random Variables]</ref>
# A Statistical Distribution must be chosen for each Random Variable in Slide2.<ref name="ref_c94e4d69" />
# The larger the Standard Deviation, then the wider the range of values which the Random Variable may assume (within the limits of the Minimum and Maximum values).<ref name="ref_c94e4d69" />
# Note that in the case of the shear strength random variable, coefficient of variation (COV) is entered instead of Standard Deviation.<ref name="ref_c94e4d69" />
# Such a number varies from trial to trial of the corresponding experiment, and does so in a way that cannot be predicted with certainty; hence, it is called a random variable.<ref name="ref_6ea3450f">[https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Book%3A_Introductory_Statistics_(Shafer_and_Zhang)/04%3A_Discrete_Random_Variables 4: Discrete Random Variables]</ref>
# Random Variables A random variable is a number generated by a random experiment.<ref name="ref_6ea3450f" />
# A random variable is called discrete if its possible values form a finite or countable set.<ref name="ref_6ea3450f" />
# The probability distribution of a discrete random variable X is a list of each possible value of X together with the probability that X takes that value in one trial of the experiment.<ref name="ref_6ea3450f" />
# We can define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space .<ref name="ref_8e343611">[https://www.varsitytutors.com/hotmath/hotmath_help/topics/random-variable Random Variable]</ref>
# In this experiment, we can define random variable X as the total number of tails.<ref name="ref_8e343611" />
# X = x ) is usually used to represent the probability of a random variable, where the X is random variable and x is one of the values of random variable.<ref name="ref_8e343611" />
# The realization that the concept of a random variable is a special case of the general concept of a measurable function came much later.<ref name="ref_1826eed8">[https://encyclopediaofmath.org/wiki/Random_variable Encyclopedia of Mathematics]</ref>
# This made it clear that a random variable is nothing but a measurable function on a probability space.<ref name="ref_1826eed8" />
# Random variable refers to a variable whose value is not known or a function which obtains its values from the outcome of a random experiment.<ref name="ref_d0f6750b">[https://cleartax.in/g/terms/random-variable Definition, Latest News, and Why Random Variable is Important?]</ref>
# The value of a random variable is not calculated like an algebraic variable.<ref name="ref_d0f6750b" />
# In probability, a real-valued function, defined over the sample space of a random experiment, is called a random variable.<ref name="ref_2e24e7c0">[https://byjus.com/maths/random-variable/ Definition, Types Formula and Example]</ref>
# A random variable’s likely values may express the possible outcomes of an experiment, which is about to be performed or the possible outcomes of a preceding experiment whose existing value is unknown.<ref name="ref_2e24e7c0" />
# The domain of a random variable is a sample space, which is represented as the collection of possible outcomes of a random event.<ref name="ref_2e24e7c0" />
# A random variable is a rule that assigns a numerical value to each outcome in a sample space.<ref name="ref_2e24e7c0" />
# Let X be a discrete random variable and Y be a continuous random variable.<ref name="ref_d7c1440a">[http://www.csam.or.kr/journal/view.html?doi=10.29220/CSAM.2020.27.3.285 Independence test of a continuous random variable and a discrete random variable]</ref>
# An exponentiated Weibull continuous random variable.<ref name="ref_23e73dc9">[https://docs.scipy.org/doc/scipy/reference/stats.html Statistical functions (scipy.stats) — SciPy v1.5.4 Reference Guide]</ref>
# A folded Cauchy continuous random variable.<ref name="ref_23e73dc9" />
# A Frechet left (or Weibull maximum) continuous random variable.<ref name="ref_23e73dc9" />
# A generalized Pareto continuous random variable.<ref name="ref_23e73dc9" />
# A random variable is a measurable mapping from the sample space asociated with a random experiment into the set of real numbers, \(X:S\mapsto{\mathbb R}\).<ref name="ref_7bd11c8d">[http://www.est.uc3m.es/icascos/eng/probability_notes/discrete-random-variables.html Chapter 2 Discrete random variables]</ref>
# The support or range of a random variable \(X(S)\) is the set of all values that it can assume.<ref name="ref_7bd11c8d" />
===소스===
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 * ID :  [https://www.wikidata.org/wiki/Q176623 Q176623]

← 이전 판		2020년 12월 26일 (토) 12:12 판
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		+	* ID : [https://www.wikidata.org/wiki/Q176623 Q176623]

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2021년 2월 17일 (수) 07:58에 Pythagoras0님의 편집

Pythagoras0: /* 메타데이터 */ 새 문단

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