Question 1197875: Classify each of the following random variables as discrete or continuous.
a) Number of times you catch a ball in a basketball game
b) Length of time you play in a basketball game
c) Length of a car in centimeters
d) Number of red cars on the highway
Answer by math_tutor2020(3816)   (Show Source):
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Answers:- Discrete
- Continuous
- Continuous
- Discrete
Explanations:
(a) The number of times you catch a ball is some nonnegative whole number {0,1,2,3,...} which means we have a discrete set here.
Between any two values is some finite subset. Eg: {1,2,3} is finite.
The midpoint of adjacent values is not valid.
It doesn't make sense to apply the midpoint between say 1 and 2 to get 1.5 catches.
(b) In contrast to (a), the midpoint is valid for any two time values.
For instance, if a basketball player plays somewhere between 10 and 11 minutes, then s/he could have played for 10.5 minutes.
This is why we consider time to be a continuous variable.
Unlike discrete variables, continuous variables have infinitely many values between any two distinct items.
(c) Same idea as part (b)
(d) Same idea as part (a)
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