classify the following as discrete or continuous random variables:
a) the time it takes to run a marathon- i think that it is discrete
b) the number of fractions between one and two- i think that it is discrete?
c) a pair of dice is rolled and the sum to appear on the dice is recorded- i think that it is discrete
d) the length of a broad jump- i think that it is continuous.
*am i correct and if not what would i need to change? please clarify with specifics. thank you.
mary hornbeck
a) If length is continuous, wouldn't time also be continuous?
b) The fractions can get smaller and smaller (e.g., 1 and 1*10^-9)
Otherwise, I think you are correct.
For your own safety, it is better not to use your whole name.
Let's analyze each scenario to determine if the random variables are discrete or continuous:
a) The time it takes to run a marathon: Your initial response is not correct. Running time for a marathon would typically be considered a continuous random variable. The time can take on any value within a range, including fractions of a second, and is not limited to a specific set of values.
b) The number of fractions between one and two: Your initial response is correct. The number of fractions between one and two is a discrete random variable. There is a set number of fractions in that range (e.g., halves, quarters, eighths), and you cannot have fractions like 1.5 or 1.75.
c) The sum appearing on a pair of dice: Your initial response is correct. The sum appearing on a pair of dice is a discrete random variable. The possible values are distinct and finite, ranging from 2 to 12 (each number representing the sum of the two dice).
d) The length of a broad jump: Your initial response is correct. The length of a broad jump is typically considered a continuous random variable. It can take on any value within a range, including decimal values. There is no restriction on the possible values it can assume.
To summarize:
a) Continuous (time it takes to run a marathon)
b) Discrete (number of fractions between one and two)
c) Discrete (sum appearing on a pair of dice)
d) Continuous (length of a broad jump)
Remember, when determining if a random variable is discrete or continuous, you should consider whether its possible values are distinct and finite (discrete) or infinite and uncountable (continuous).