Chapter four

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
2. **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.
   2. 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)
   3. Variance of Discrete Random Variables
      1. SD^2 = ∑(x - µ)^2 • P(x)

1. SSO

   Annotations:

   • Sample Space Outcomes
2. Experiment

   Annotations:

   • A Random non-determined experiment.
3. Variable

   Annotations:

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

   Annotations:

   • How many times you did the experiment
5. 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)?
6. event of interest

1. Binomial Formula

Attachments:

• Discrete Probability Distributions

1. (p)

   Annotations:

   • Sucess
2. (q)

   Annotations:

   • Failure
3. (x)

   Annotations:

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

   Annotations:

   • Number of trials
5. (X)

   Annotations:

   • The event of interest

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

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.
   2. 2)Trials results (S) (F)
      1. Success
      2. Failure

         Annotations:

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