Chapitre_3_ecris
DownloadTélécharger
Actions
Vote :
ScreenshotAperçu
Informations
Catégorie :Category: nCreator TI-Nspire
Auteur Author: Nass23232
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 3.65 Ko KB
Mis en ligne Uploaded: 20/12/2019 - 06:49:11
Mis à jour Updated: 20/12/2019 - 06:49:19
Uploadeur Uploader: Nass23232 (Profil)
Téléchargements Downloads: 51
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a2528086
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 3.65 Ko KB
Mis en ligne Uploaded: 20/12/2019 - 06:49:11
Mis à jour Updated: 20/12/2019 - 06:49:19
Uploadeur Uploader: Nass23232 (Profil)
Téléchargements Downloads: 51
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a2528086
Description
Fichier Nspire généré sur TI-Planet.org.
Compatible OS 3.0 et ultérieurs.
<<
1) Basis: Bernoulli random variable Definition: random variable with only two outcomes ( success and failure ) Probability of these outcomes satisfies the conditions for a valid pdf. That is, each probability is between 0 and 1 and they sum to 1. Single observation of a Bernoulli random variable = trial when the random variable can repeat. (2) Binomial distribution × Consider n trials of a Bernoulli experiment (remembre: only two outcomes success and failure ) × Binomial variable X = number of successes in n Bernoulli trials, i,. e. the sum of a series of Bernoulli trials is distributed as a binomial random variable. × In order to use the binomial distribution, we must satisfy two conditions: 1. Theprobabilityofeachoutcomemustbeconstantforalltrials;and 2. Thetrialsmustbeindependent. × Given these assumtions, the distribution of a binomial random variable is described by just two parameters: the number of trials (n) and the probability of a successful trial (p) (3) Mean and variance of binomial distribution Remember: Binomial random variable X Shows number of successes in n Bernoulli trials, i,. e. the sum of a series of Bernoulli trials is distributed as a binomial random variable. pdf completely described by two parameters, n and p: X < B(n, p) Then: a Bernoulli random variable can be seen as a binomial variable Y with n =1 trial only 3.3 Continuous Random Variables Recall properties of continuous random variables: Possible outcomes cannot be counted Given an outcome, e. g., X = 250, the next higher or lower value cannot be named " Probability of any given value equals zero 3.3.1 Continuous Uniform Distribution continuous counterpart to the discrete uniform distribution: it also describes equally likely outcomes - we believe that all possible outcomes are equally likely - ... we have no prior information or beliefs about the distribution of probability over outcomes When we want to generate random numbers in simulations: here, this distribution is almost always the basis for generating random numbers in simulations; hence, it is a very important distribution. 3.3.2 Normal Distribution (1) Relevance × single most important distribution in statistics × Reasons: It plays a key role in modern portfolio theory and risk management. The central limit theorem demonstrates that the sum and mean of a large number of independent random variables will be normally distributed even when the variables are not themselves normally distributed. It is often used as a model for approximate returns. Linear combinations of normally distributed variables are also normally distributed. (2) Defining characteristics × × × - - continuous, symmetrical distribution ranges from infinitely negative to infinitely positive. Completely described by its mean and variance w e indicate that a random variable is normally distributed as ýý ~ ýý (¼, à 2 ) Symmetrical , i. e., skewness = 0 m ean = median = mode Note: Option returns are skewed; they are not normally distributed. Kurtosis of 3 or excess kurtosis of 0. Univariate versus multivariate distribution × × × A single random variable is said to be univariately distributed. A group of related random variables is said to be multivariately distributed. example: a group of two random variables would have a bivariate distribution. The multivariate normal distribution is common in portfolio applications : If individual security returns are jointly, normally distributed, then the total returns of a portfolio of these securities will also be normally distributed and we can describe the probability behavior of that portfolio with the information in the list . To characterize a multivariate normal distribution, we need: 1. Thelistofmeanreturnsforeachsecurity; The list of variances in those returns for each security; (4) Standard normal distribution = normal distribution with a mean of ¼ = 0 and standard deviation of à = 1 × × × Idea: refer all probability statements about normally distributed variables to a single normal distribution Action: create a standard normal distribution and use probability tables calculated for that standard normal distribution standardizing is accomplished by: 1. Takingtheobservation(s)ofinterest(X)andsubtractingthemean (¼) of that observations observed distribution; 2. Dividingtheresultbytheobserved distributions standard deviation(Ã). this leads to the standard -normally distributed variable Z which replaces X Made with nCreator - tiplanet.org
>>
Compatible OS 3.0 et ultérieurs.
<<
1) Basis: Bernoulli random variable Definition: random variable with only two outcomes ( success and failure ) Probability of these outcomes satisfies the conditions for a valid pdf. That is, each probability is between 0 and 1 and they sum to 1. Single observation of a Bernoulli random variable = trial when the random variable can repeat. (2) Binomial distribution × Consider n trials of a Bernoulli experiment (remembre: only two outcomes success and failure ) × Binomial variable X = number of successes in n Bernoulli trials, i,. e. the sum of a series of Bernoulli trials is distributed as a binomial random variable. × In order to use the binomial distribution, we must satisfy two conditions: 1. Theprobabilityofeachoutcomemustbeconstantforalltrials;and 2. Thetrialsmustbeindependent. × Given these assumtions, the distribution of a binomial random variable is described by just two parameters: the number of trials (n) and the probability of a successful trial (p) (3) Mean and variance of binomial distribution Remember: Binomial random variable X Shows number of successes in n Bernoulli trials, i,. e. the sum of a series of Bernoulli trials is distributed as a binomial random variable. pdf completely described by two parameters, n and p: X < B(n, p) Then: a Bernoulli random variable can be seen as a binomial variable Y with n =1 trial only 3.3 Continuous Random Variables Recall properties of continuous random variables: Possible outcomes cannot be counted Given an outcome, e. g., X = 250, the next higher or lower value cannot be named " Probability of any given value equals zero 3.3.1 Continuous Uniform Distribution continuous counterpart to the discrete uniform distribution: it also describes equally likely outcomes - we believe that all possible outcomes are equally likely - ... we have no prior information or beliefs about the distribution of probability over outcomes When we want to generate random numbers in simulations: here, this distribution is almost always the basis for generating random numbers in simulations; hence, it is a very important distribution. 3.3.2 Normal Distribution (1) Relevance × single most important distribution in statistics × Reasons: It plays a key role in modern portfolio theory and risk management. The central limit theorem demonstrates that the sum and mean of a large number of independent random variables will be normally distributed even when the variables are not themselves normally distributed. It is often used as a model for approximate returns. Linear combinations of normally distributed variables are also normally distributed. (2) Defining characteristics × × × - - continuous, symmetrical distribution ranges from infinitely negative to infinitely positive. Completely described by its mean and variance w e indicate that a random variable is normally distributed as ýý ~ ýý (¼, à 2 ) Symmetrical , i. e., skewness = 0 m ean = median = mode Note: Option returns are skewed; they are not normally distributed. Kurtosis of 3 or excess kurtosis of 0. Univariate versus multivariate distribution × × × A single random variable is said to be univariately distributed. A group of related random variables is said to be multivariately distributed. example: a group of two random variables would have a bivariate distribution. The multivariate normal distribution is common in portfolio applications : If individual security returns are jointly, normally distributed, then the total returns of a portfolio of these securities will also be normally distributed and we can describe the probability behavior of that portfolio with the information in the list . To characterize a multivariate normal distribution, we need: 1. Thelistofmeanreturnsforeachsecurity; The list of variances in those returns for each security; (4) Standard normal distribution = normal distribution with a mean of ¼ = 0 and standard deviation of à = 1 × × × Idea: refer all probability statements about normally distributed variables to a single normal distribution Action: create a standard normal distribution and use probability tables calculated for that standard normal distribution standardizing is accomplished by: 1. Takingtheobservation(s)ofinterest(X)andsubtractingthemean (¼) of that observations observed distribution; 2. Dividingtheresultbytheobserved distributions standard deviation(Ã). this leads to the standard -normally distributed variable Z which replaces X Made with nCreator - tiplanet.org
>>
