Sample Space
In probability theory, a sample space is the set of all possible outcomes of a random experiment or a statistical study
In probability theory, a sample space is the set of all possible outcomes of a random experiment or a statistical study. It is denoted by the symbol “S”.
To understand the concept of a sample space, let’s consider an example. Suppose you roll a fair six-sided die. The possible outcomes of this experiment are rolling a 1, 2, 3, 4, 5, or 6. The sample space, in this case, would be {1, 2, 3, 4, 5, 6}.
The sample space can be finite or infinite, depending on the experiment. For example, if you toss a coin once, the sample space would be {Heads, Tails}, a finite sample space. On the other hand, if you randomly select a real number between 0 and 1, the sample space would be an infinite interval [0, 1], representing all possible real numbers between 0 and 1.
In more complex experiments, the sample space can be formed by combining the sample spaces of multiple independent events. For example, if you roll two dice, the sample space would be the set of all possible pairs of outcomes for both dice. It would consist of 36 possible outcomes, such as (1, 1), (1, 2), (1, 3), …, (6, 6).
Understanding the sample space is crucial in probability theory as it allows us to determine the likelihood of various events occurring. By identifying the sample space, we can assign probabilities to individual outcomes and calculate the probability of events of interest.
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