The mean of a discrete random variable x is the mean we would expect if the experiment were repeated many times.

The mean value is denoted by μ and obtained with the formula μ = ΣxP (x)

Another term for the mean value of a discrete random variable is expected value.

The expected value is denoted by E (x), i.e. E (x) = ΣxP (x)

In the lesson on the probability distribution of a discrete random variable, we have the following table of probability distribution. Use it to calculate the average 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 P (x) = 1

How to find the mean of the probability distribution of the number of vehicles people own.

 x P (x) xP (x) = x × P (x) 0 0.2 0x0.2 = 0 1 0.5 1 x 0.5 = 0.5 2 0.3 2 x 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? That means, on average, you would expect people to own around 1.1 vehicles.

## Another example showing how to find the mean of a discrete random variable

A survey was carried out to find out how often people go to the cinema each week. After interviewing 500 people, the result is shown in the following table. Let x be the number of visits to the cinema per week. If x = 2, the frequency is 75. This means that 75 people went to the cinema twice a week.

 x frequency 0 250 1 125 2 75 3 45 4th 5 N = 500

P (x = 0) = 250/500 = 0.5
P (x = 1) = 125/500 = 0.25
P (x = 2) = 75/500 = 0.15
p (x = 3) = 45/500 = 0.09
P (x = 4) = 5/500 = 0.01

The following table shows the probability distribution.

 x P (x) 0 0.5 1 0.25 2 0.15 3 0.09 4th 0.01 P (x) = 1

How to find the mean for the probability distribution of how often people go to the movies.

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 average number of admissions per week is 0.86.

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