Chapter four

Chapter four

1. Random Variables

   • A random variable can be thought of as representing an uncertain numerical outcome of an experiment
   • Continuous random variable
     • 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
   • **Discrete random variables**
     • Counting numbers like rolling dice or flipping a coin.
     • Methods for discribing
       • 1) histograms, X and it's corresponding values in a probability table and a function.
     • The mean
       • The Average value of the random variable if we were to observe it for an indefinite period of time
       • µ = ∑xP(x)
     • Variance of Discrete Random Variables
       • SD^2 = ∑(x - µ)^2 • P(x)

2. Definitions

   • SSO
     • Sample Space Outcomes
   • Experiment
     • A Random non-determined experiment.
   • Variable
     • 1)A description of a person/place/idea 2) This value can vary from one entity to another
   • Trials
     • How many times you did the experiment
   • Probability Distribution
     • list of all possible outcomes of a RANDOM VARIABLE
     • Coin Example
       • flip a coin 3 times... Let A= the even of observing 1 heads in three flips.
       • What is the P(A)?
   • event of interest

3. Formulas

   • Binomial Formula

4. calling it that

   • Discrete Probability Distributions
   • (p)
     • Sucess
   • (q)
     • Failure
   • (x)
     • Total number of successes in (n) trials
   • (n)
     • Number of trials
   • (X)
     • The event of interest

5. Probability Distribution Table

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

6. **Binomial random variables**

   • n trials where the probability for a success for each trial is p, the probability of observing x successes is?
   • Characteristics
     • 1) Identical Trials
       • The trials are the exact same.
     • 2)Trials results (S) (F)
       • Success
       • Failure
         • 1-P
     • 3) probability (p) is constant from trial to trial
     • 4)The trials are independent
   • Binomial probability mass function
     • P(x) = nCx • px • (1-p)^(n-x)
     • MU= N x P
     • SD^2 = np(1 - p)

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