Chapter 4 – Probability concepts. This chapter define a random variable, an outcome, an event, mutually exclusive events, and exhaustive events; explain the two defining properties of probability; distinguish among empirical, subjective, and a priori probabilities; state the probability of an event in terms of odds for or against the event;. | Probability concepts Introduction Fundamental Concepts A variable is random if its outcome is uncertain, where an outcome is an observable future value of the variable. An event is the specified set of possible outcomes of a random variable. Events are mutually exclusive when the possible future outcomes can only occur one at a time and exhaustive when the set of outcomes includes every possible value the variable could take in the future. Example: The future size of a dividend can be stated as a mutually exclusive and exhaustive event wherein dividends increase, decrease, or remain unchanged. When the occurrence of one event does not affect the probability of the occurrence of another event, we say the events are independent. Events that are not independent are dependent. 2 LOS: Define a random variable, an outcome, an event, mutually exclusive events, and exhaustive events. Pages 129–130 Randomness and dependence/independence are of particular importance because they appear . | Probability concepts Introduction Fundamental Concepts A variable is random if its outcome is uncertain, where an outcome is an observable future value of the variable. An event is the specified set of possible outcomes of a random variable. Events are mutually exclusive when the possible future outcomes can only occur one at a time and exhaustive when the set of outcomes includes every possible value the variable could take in the future. Example: The future size of a dividend can be stated as a mutually exclusive and exhaustive event wherein dividends increase, decrease, or remain unchanged. When the occurrence of one event does not affect the probability of the occurrence of another event, we say the events are independent. Events that are not independent are dependent. 2 LOS: Define a random variable, an outcome, an event, mutually exclusive events, and exhaustive events. Pages 129–130 Randomness and dependence/independence are of particular importance because they appear regularly and are an important feature of sampling theory; they ensure the underlying characteristics of the statistics we will spend time learning and using. 2 Probability Probability is the fundamental building block of statistics. Probability is a number between 0 and 1 that describes the chance that a stated event from the set of possible outcomes will occur. A probability distribution is the set of probabilities and their associated outcomes that describes all possible outcomes and their associated probabilities. We typically use P(E) to denote the probability of event E. Properties of probability All probabilities must lie between 0 and 1: For n mutually exclusive and exhaustive events, the sum of all probabilities must equal 1: 3 LOS: Explain the two defining properties of probability. Page 130 3 Types of probability Sources of probabilities In practice, we observe a number of different types of probability. A subjective probability is a personal assessment of the likelihood of an event
