Classify the following random variables as discrete or continuous:X: the number of automobile accidents per year in Virginia. Y
: the length of timeto play 18 holes of golf. M: the amount of milk produced yearly by a particular cow.N: the number of eggs laid each month by a hen. P: the number of building permitsissued each month in a certain city. Q: the weight of grain produced per acre.
First, we have to know the difference between discrete and continuous variables:
Discrete variables are those that represent things that are counted, 3 red cars, 2 chickens, etc.. They take positive integer values, {0, 1, 2, ..., n}, being [0, n] the interval from which the variable takes values, that means, there is a finite number of possible values.
Continuous variables are those that represent things that are measured, 3.56 km of railway laid, 5.77 l of paint used. They take positive real values, that means that in the interval used for the variable there are infinite possible values.
Now, we classify each variable:
The number of automobile accidents per year in Virginia (X) is a discrete variable, as there can't be half an accident, one counts how many accidents are per year to know X.
The length of time to play 18 holes of golf (Y) is a continuous variable, as it can take 2 hours, or 2.5 hours, or 2 hours, 30 minutes, 2 seconds, one measures how long it took to play 18 holes to know Y.
The amount of milk produced yearly by a particular cow (M) is a continuous variable, as one measures how much milk was produced to know M.
The number of eggs laid each month by a hen (N) is a discrete variable, as one counts how much eggs were laid to know N.
The number of building permits issued each month in a certain city (P) is a discrete variable, as one counts how many permits were issued to know P.
The weight of grain produced per acre (Q) is a continuous variable, as one measures the weight per acre to know Q.
