EDA-Lesson 6

• Discrete Sample Space


  A sample space is discrete if it consists of a finite or countable infinite set of outcomes
• Event

  Subset of the sample space of a random experiment
• Random Experiment


  An experiment that can result in different outcomes, even though it is repeated in the same manner every time
• Probability Models

  • Theoretical Probability: Predicts the likelihood of an event occurring in ideal conditions
  • Experimental Probability: Determined through empirical observation and experimentation, based on actual outcomes
  • Subjective Probability: Involves personal judgment or belief about the likelihood of an event occurring
• Mutually Exclusive Events


  E1 ∩ E2 = ∅
• Intersection of two events


  1. Consists of all outcomes that are contained in both of the two events

  2. Denoted by E1 ∩ E2
• Continuous Sample Space

  A sample space is continuous if it contains an interval (either finite or infinite) of real numbers
• Probability

  • A tool to relate the descriptive statistics to inferential statistics
  • Ratio of number of samples derived from the total population
  • Deals with counting elements
  • Fundamental concept in mathematics that deals with the likelihood of events occurring
• Union of two events


  1. Consists of all outcomes that are contained in either of the two events

  2. Denoted by E1 ∪ E2
• Sample Space


  • The set of all possible outcomes of a random experiment
  • Denoted as S
• Counting Techniques

  1. Multiplication Rule: If an operation can be performed in 𝑛1 ways, and if for each of these a second operation can be performed in 𝑛2 ways, then the two operations can be performed in 𝑛1𝑛2 ways.

  2. Permutation: An ordered sequence of the elements

  3. Permutation of Subsets = P(n,r) = n! / (n-r)!

  4. Circular Permutation = (n-1)!

  5. Combination: A combination is actually a partition of two cells, the one cell containing the 𝑟 objects selected and the other cell containing the 𝑛 − 𝑟 objects that are left

  6. C(n, r) = n1/ r! (n-r)!
• Complement of an event

  1. Set of outcomes in the sample space that are not in the event

  2. The complement of the event E is E′ or E^C

  3. (E′)′ = E