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The mean of a discrete random variable x is the average value that we would expect to get if the experiment is repeated a large number of times.
The mean is denoted by μ and obtained using the formula μ = ΣxP(x)
Another name for the mean of a discrete random variable is expected value.
The expected value is denoted by E(x), so E(x) = ΣxP(x)
In the lesson about probability distribution of a discrete random variable, we have the probability distribution table below. Use it to compute the mean number of vehicles owned by people.
| Number of vehicles owned or x | Probability or P(x) |
| 0 | 0.2 |
| 1 | 0.5 |
| 2 | 0.3 |
| ΣP(x) = 1 |
Here is how to calculate the mean for the probability distribution of number of vehicles owned by people.
| x | P(x) | xP(x) = x × P(x) |
| 0 | 0.2 | 0 × 0.2 = 0 |
| 1 | 0.5 | 1 × 0.5 = 0.5 |
| 2 | 0.3 | 2 × 0.3 = 0.6 |
| ΣxP(x) = 0 + 0.5 + 0.6 = 1.1 |
E(x) = 1.1
What does an expected value of 1.1 mean for this situation? It means that on average, you would expect people to own about 1.1 vehicles.
A survey was conducted to find out how many times people go to the movie theater per week. After interviewing 500 people, the result is shown in the table below. Let x be the number of times people go to the movie theater per week. When x = 2, the frequency is 75. This means that 75 people went to the movie theater twice per week.
| x | Frequency |
| 0 | 250 |
| 1 | 125 |
| 2 | 75 |
| 3 | 45 |
| 4 | 5 |
| N = 500 |
The table below shows the probability distribution.
| x | P(x) |
| 0 | 0.5 |
| 1 | 0.25 |
| 2 | 0.15 |
| 3 | 0.09 |
| 4 | 0.01 |
| ΣP(x) = 1 |
E(x) = ΣxP(x) = 0 × 0.5 + 1 × 0.25 + 2 × 0.15 + 3 × 0.09 + 4 × 0.01
E(x) = 0 + 0.25 + 0.30 + 0.27 + 0.04
E(x) = 0.86
Based on the expected value of 0.86, the mean number of times people will go to the movie theater per week is 0.86.