random variables

Question

The sum of all probabilities in a probability distribution equals

RankGuru · Accepted Answer

1. **Total Certainty**: A probability distribution assigns probabilities to all possible outcomes of an experiment. Since one of these outcomes **must** occur, the total probability is certainty.
2. **Axiom**: $\sum P(X = x_i) = 1$.
3. **Continuous Case**: $\int_{-\infty}^{\infty} f(x) dx = 1$.
4. **Conclusion**: The total area under a probability density curve or sum of discrete mass is always **1**.

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random variables

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