sample space
In probability theory, the sample space refers to the set of all possible outcomes of an experiment or a random event
In probability theory, the sample space refers to the set of all possible outcomes of an experiment or a random event. It is denoted by the symbol “S”. Essentially, the sample space encompasses all the potential results that can occur when conducting a particular experiment.
The sample space can be either discrete or continuous. A discrete sample space consists of a countable number of distinct outcomes, such as rolling a six-sided die and getting one of the numbers from 1 to 6. On the other hand, a continuous sample space involves a range of possible outcomes that can take on any value within a certain interval, such as measuring the height of individuals in a population.
When describing the sample space, it is important to define it accurately and comprehensively. This means considering all possible outcomes, including any potential surprising events. Additionally, the sample space should be mutually exclusive, meaning that no two outcomes can occur simultaneously.
Understanding the sample space is crucial in probability theory as it lays the foundation for calculating probabilities and making predictions about the likelihood of specific events occurring. By identifying all the possible outcomes and assigning probabilities to each of them, we can analyze events, make informed decisions, and draw conclusions based on data and experimentation.
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