Answer: To find the mean of a probability distribution, multiply each possible outcome by its corresponding probability, then sum up these products.

Mathematically, it can be represented as:

Mean (μ) = Σ (x × P(x))

Where:

• μ is the mean
• x represents each possible outcome
• P(x) is the probability of each outcome

For example, consider a probability distribution with outcomes {1, 2, 3} and probabilities {0.3, 0.5, 0.2} respectively. The mean would be calculated as:

Mean (μ) = (1× 0.3) + (2 × 0.5) + (3 × 0.2) = 0.3 + 1.0 + 0.6 = 1.9

So, the mean of the probability distribution is 1.9.

In conclusion, the mean of a probability distribution is obtained by summing the products of each outcome and its probability.