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)|
|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.
|N = 500|
The table below shows the probability distribution.
|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.