Chapter four

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Statistics Mind Map on Chapter four, created by alistairewart on 19/10/2013.
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Chapter four
  1. Random Variables

    Annotations:

    • A random variable can be thought of as representing an uncertain numerical outcome of an experiment
    1. Continuous random variable

      Annotations:

      • variables can take any numerical value on the real number line
      • temperature of a cup of coffee served at mcdonald's restaurant.
      • time in seconds that a customer in a store must wait to recieve a cred card autorization
      • any value is possible in a certain range
      1. **Discrete random variables**

        Annotations:

        • Counting numbers like rolling dice or flipping a coin.
        1. Methods for discribing

          Annotations:

          • 1) histograms, X and it's corresponding values in a probability table and a function.
          1. The mean

            Annotations:

            • The Average value of the random variable if we were to observe it for an indefinite period of time
            1. µ = ∑xP(x)
            2. Variance of Discrete Random Variables
              1. SD^2 = ∑(x - µ)^2 • P(x)
          2. Definitions
            1. SSO

              Annotations:

              • Sample Space Outcomes
              1. Experiment

                Annotations:

                • A Random non-determined experiment.
                1. Variable

                  Annotations:

                  • 1)A description of a person/place/idea 2) This value can vary from one entity to another
                  1. Trials

                    Annotations:

                    • How many times you did the experiment
                    1. Probability Distribution

                      Annotations:

                      • list of all possible outcomes of a RANDOM VARIABLE
                      1. Coin Example

                        Annotations:

                        • flip a coin 3 times... Let A= the even of observing 1 heads in three flips.
                        • What is the P(A)?
                      2. event of interest
                      3. Formulas
                        1. Binomial Formula
                        2. calling it that

                          Attachments:

                          1. (p)

                            Annotations:

                            • Sucess
                            1. (q)

                              Annotations:

                              • Failure
                              1. (x)

                                Annotations:

                                • Total number of successes in (n) trials
                                1. (n)

                                  Annotations:

                                  • Number of trials
                                  1. (X)

                                    Annotations:

                                    • The event of interest
                                  2. Probability Distribution Table

                                    Annotations:

                                    • is a list of all possible outcomes of a random variable and their corresponding probabilities
                                    1. Setting up

                                      Annotations:

                                      • 1) define the random variable x= event of interest
                                      • 2) create a table of outcomes with the two headings outcomes and value of X
                                      • 3) list all of the possible outcomes and the values of X that correspond to each
                                      • 4) create probability distribution table with three headings x, frequency, m, P(x)
                                      • Remember to put totals at the end of the graph
                                    2. **Binomial random variables**

                                      Annotations:

                                      • n trials where the probability for a success for each trial is p, the probability of observing x successes is?
                                      1. Characteristics
                                        1. 1) Identical Trials

                                          Annotations:

                                          • The trials are the exact same.
                                          1. 2)Trials results (S) (F)
                                            1. Success
                                              1. Failure

                                                Annotations:

                                                • 1-P
                                              2. 3) probability (p) is constant from trial to trial
                                                1. 4)The trials are independent
                                                2. Binomial probability mass function
                                                  1. P(x) = nCx • px • (1-p)^(n-x)
                                                    1. MU= N x P
                                                      1. SD^2 = np(1 - p)
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