Probability distribution of a discrete random variable
The probability distribution of a discrete random variable shows all possible values a discrete random variable can have along with their corresponding probabilities.￼ You could use a table to organize the information.
In the lesson about discrete random variable, you conducted a survey asking 200 people about the number of vehicles they own. You came up with the following result.
40 people say that they don’t own a car, 100 say they own 1, and 60 say they own 2.
You could start with a table showing the frequency and relative frequency distribution.
The relative frequency for owning 0 vehicle is 40/200 = 0.2
The relative frequency for owning 1 vehicle is 100/200 = 0.5
The relative frequency for owning 2 vehicles is 60/200 = 0.3
|Number of vehicles owned||Frequency distribution||Relative frequency distribution|
|N =200||Sum = 1|
From the table above, we can pull out the probability distribution. Recall that it will list all the possible values for the random variable and their corresponding probabilities.
|Number of vehicles owned or x||Probability or P(x)|
Characteristics of the probability distribution of a discrete random variable
You may have noticed the following 2 characteristics after a close examination of the table above.
- The probability assigned to each value of a discrete random variable is between 0 and 1 inclusively. In other words, 0 ≤ P(x) ≤1.
- The sum of the probabilities is equal to 1.
The meaning of P(x = 1) is probability that a randomly selected person owns 1 car.
P(x = 1) = 0.5
The meaning of P(x > 0) is probability that a randomly selected person owns at least 1 car.
P(x > 0 ) = P(x = 1) + P(x = 2) = 0.5 + 0.3 = 0.8