Final answer:
The expected value or mean of a discrete random variable is calculated by summing the products of each possible value and its corresponding probability. For example, if a soccer team plays 0, 1, or 2 days a week with corresponding probabilities of 0, 0.5, and 0.6, the expected number of play days would be 1.7.
Step-by-step explanation:
Calculating the Expected Value of a Discrete Random Variable
To calculate the expected value or mean (μ) of a discrete random variable y, you would need to use the following formula: E(y) = μ = Σ yP(y). This involves multiplying each possible value of y by its corresponding probability P(y) and then summing all these products together. For instance, in a table with values of y and their probabilities, you add an additional column that contains the products of y and P(y). The sum of this column will provide the expected value of the random variable, representing the long-term average you would expect after many repetitions of the experiment.
An example would be calculating the expected number of days per week a soccer team plays. If the team plays no days with a probability of 0, plays one day with a probability of 0.5, and two days with a probability of 0.6, the expected number of play days would be 0*(0) + 1*(0.5) + 2*(0.6) = 1.7 days. Thus, the expected value/mean is 1.7, signifying the team would expect to play soccer 1.7 days per week on average.