Stats and Prob-Random Variables and Probability Distribution

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Cards (20)

  • STATISTICS is a science that deals with the collection, analysis, and interpretation of data.
  • The field of statistics is divided into two major divisions called descriptive statistics and inferential statistics.
  • DESCRIPTIVE STATISTICS -- In this type of statistics, numerical measures are used to talk about features of a set of data or to summarize the characteristics of a given data set. It consists of methods for organizing and summarizing information.
  • INFERENTIAL STATISTICS -- Inferential statistics are tools that are used to draw conclusions about the characteristics of a population and to decide how certain they can be of the reliability of those conclusions. It consists of methods for drawing and measuring the reliability of conclusions about a population based on information obtained from a sample of the population.
  • PROBABILITY is a field of mathematics that deals with the chance (the likelihood) of an event occurring.
  • EXPERIMENT -- It is an action whose outcome cannot be predicted with certainty.
  • OUTCOME -- possible result of an experiment or trial
  • EVENT -- Collection of outcomes wherein some specified result may or may not occur when an experiment is performed
  • SAMPLE SPACE -- It is a set that contains all possible outcomes of an experiment. Typically denoted by 𝑆.
  • Probability of an event, 𝑃(𝐸) =n(E)/n(S)
  • n(E) = no. of ways an event can occur
    n(S) = π‘‡π‘œπ‘‘π‘Žπ‘™ π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘π‘œπ‘ π‘ π‘–π‘π‘™π‘’ π‘œπ‘’π‘‘π‘π‘œπ‘šπ‘’π‘ 
  • RANDOM VARIABLE
    It is a (quantitative) variable** whose value depends on chance.
    It is a set whose elements are numerical outcomes of an experiment. A function that associates a numerical value with every outcome of an experiment.
    Its domain is a sample space, and its range is some set of real numbers.Β 
    We use UPPERCASE LETTERS to represent a random
    variable.Β 
    A random variable is a result of chance event, that you can measure or count.
  • An uppercase letter, commonly X , is used to denote a random variable,
    while the corresponding lowercase letter x is used to denote one of the values of a random variable. A random variable has either a probability distribution for a discrete random variable or a probability density function for a continuous random variable.
  • VARIABLE -- A characteristic/attribute that varies from one person or thing to another.
  • VARIABLE=(QUALITATIVE), QUANTITATIVE-(CONTINUOUS,DISCRETE)
  • [1]Β Β Β  DISCRETE RANDOM VARIABLE
    -Β Β Β Β Β  It can take only a finite number of distinct values.
    -Β Β Β Β Β  β€œCOUNTABLE”
  • [2]Β Β Β  CONTINUOUS RANDOM VARIABLE
    -Β Β Β Β Β  It can take on any value in an interval.
    -Β Β Β Β Β  β€œMEASUREABLE”
  • PROBABILITY DISTRIBUTIONS OF A DISCRETE RANDOM VARIABLE
    @also known as probability mass
    function/probability distribution function.
    @ It is a list, a table, a graph, or a formula of probabilities associated with each of its possible values
  • Β  The probability of each outcome is between 0 and 1, inclusive. That is, 𝟎𝟎 ≀ 𝑃(outcome) ≀ 1
  • Β Β Β Β Β Β  The sum of all the probabilities of the random
    variable is equal to 1 or 100%. That is,
    βˆ‘π‘ƒ(X = π‘₯𝑖) = 1