MATH: STATISTICS LESSON 1

• an experiment is a situation that results into different outcomes
• an outcome in the given experiment is the result
• A sample space is a set of all possible outcomes
• Each elements is called a sample point
• An event is a single outcome or a group of outcomes
• An experiment is a process that, when performed, results in one one and and only one of many observations These observations are called the outcomes of the experiment. The collection of all outcomes for an experiment is called a sample space.
• An event is a collection of one or more of the outcomes of an experiment
• An event that includes one and only one of the (final) outcomes for an experiment is called a simple event and is denoted by E.
• A compound event is a collection of more than one outcome for an experiment
• Probability is a numerical measure of the likelihood that a specific event will occur
• TWO PROPERTIES OF PROBABILITY 1) The probability of an event always lie in the range 0 to 1 2) The sum events of the probabilities of all simple events or final outcomes for an experiment is denoted by Summation of P(Ei), is always 1
• Three Conceptual Approaches to probability 1. Classical probability 2. the relative frequency concept of probability 3. the subjective probability concept
• CLASSICAL PROBABILITY -Two or more outcomes (or events) that have the same probability of occurrence are said to be equally likely outcomes
• RELATIVE FREQUENCY CONCEPT OF PROBABILITY If an experiment is repeater in times and an event A is observed f times, then according to the relative frequency concept of probability, P(A) = f/n
• SUBJECTIVE PROBABILITY

  -Is the probability assigned to an event based on subjective judgment, experience, information, and belief
• Experiment - is an activity or process with an observable result
• Outcome - is the observable result in your experiment
• Sample Space - is the set of all results of an experiment or the set of all outcomes
• Event - is a subset or a part of your sample space
• Simple event - is a specific outcome, just one of the possible outcomes of the experiment
• Probability - is the measure of the likelihood that an event will occur
• COUNTING TECHNIQUES

  1. Grid Table
  2. Tree Diagram
  3. The fundamental principle of counting
  4. Systematic listing
• Grid table-gives us excellent visual displays of Sample spaces. It consists of columns and rows that represent seperate types of events. It is! helpful when the experiment is a two-part task.
• Tree diagram is a graphic organizer used to list all possibilities of a sequence of events in a systematic way.
• the fundamental principle of counting -of one thing can occur in m ways and a second thing can occur in n ways, and a 3rd thing can occur in p ways, and so on, then the sequence of things can occur in mxnxp ways....
• Systematic listing

  -is the process of getting the Sample Space of getting experiment where the outcome of an event is listed systematically of in an organized manner.