Final answer:
The expected value of the probability of a state is the average value that a random variable takes on, weighted by the probabilities of each possible value.
Step-by-step explanation:
The expected value of the probability of a state, denoted as E(X), is the average value that a random variable X takes on, weighted by the probabilities of each possible value.
To calculate the expected value, you multiply each possible value of the random variable by its corresponding probability, and then sum up these products.
- The formula for calculating the expected value of a discrete random variable is: E(X) = Σ x * P(x), where x represents each possible value and P(x) represents the probability of each value.
- For example, if there are three possible values for X: 1, 2, and 3, with probabilities of 0.4, 0.3, and 0.3, respectively, the expected value would be: E(X) = 1 * 0.4 + 2 * 0.3 + 3 * 0.3 = 1.7.