Sure! Here are definitions for the terms you've requested:
a. Probability: Probability is a measure or estimation of the likelihood that a particular event will occur. It is quantified as a number between 0 and 1, where 0 indicates that the event will not occur and 1 indicates that the event will certainly occur. In mathematical terms, the probability \( P \) of an event \( A \) can be expressed as \( P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \).
b. Event: An event is a specific outcome or a set of outcomes from a random experiment. It can be as simple as a single outcome (like rolling a die and getting a 3) or a combination of outcomes (like rolling an even number). Events are often denoted by capital letters (for example, \( A \), \( B \), etc.).
c. Sample Space: The sample space is the set of all possible outcomes of a random experiment. It is usually denoted by the symbol \( S \). For example, in the case of rolling a six-sided die, the sample space is \( S = {1, 2, 3, 4, 5, 6} \).
d. Probability Distribution: A probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in a sample space. It describes how probabilities are distributed over the values of a random variable. There are two main types of probability distributions: discrete probability distributions (for discrete random variables) and continuous probability distributions (for continuous random variables). Examples include the binomial distribution, the normal distribution, and the uniform distribution.
These terms are foundational concepts in probability theory and statistics.
1 answer