What is the expected outcome when developing a probability distribution for a random variable in a statistics unit?

Developing a probability distribution for a random variable serves multiple important purposes in statistics. The expected outcome includes calculating theoretical probabilities and finding the expected value, effectively combining two fundamental aspects of statistical analysis.

When a probability distribution is defined, it lays out the probabilities of occurrence for different possible outcomes of a random variable. This foundation allows for the calculation of theoretical probabilities, which are essential for understanding how likely different events are within a given population or sample space. It establishes a framework where each outcome is associated with a specific probability.

Additionally, the concept of expected value derives directly from this probability distribution. The expected value is essentially a weighted average of all possible outcomes, with each outcome's weight being its associated probability. This measure provides insight into the long-term average or mean of the random variable when the probability distribution is applied over repeated trials or observations.

Thus, the correct choice effectively encapsulates the dual purpose of developing a probability distribution: it enables the calculation of theoretical probabilities and the derivation of the expected value. This comprehensive understanding of the random variable's behavior is crucial for making informed statistical conclusions and decisions.