How To Find Mean of Probability Distribution?

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

Mathematically, it is represented as:

Mean(μ) = ​x_i – P(x_i)

Where:

• μ is the mean of the probability distribution.
• x_i represents each possible outcome.
• P(x_i) is the probability of each outcome.
• n is the total number of possible outcomes.

For example, let’s say we have a discrete probability distribution with outcomes {1, 2, 3} and probabilities {0.2, 0.5, 0.3} respectively. Then, the mean is calculated as:

μ = (1×0.2) + (2×0.5) + (3×0.3) =0.2 + 1.0 + 0.9 = 2.1

Therefore, the mean of the probability distribution is 2.1.

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