Question

exercise 3: what is that again? complete the table below.

guide question:

1. which of the examples in the table are discrete? how about continuous?

Explanation:

• Discrete random variables have countable possible values.
• Continuous random variables can take any value in an interval.

For experiment 1 (tossing a pair of coins), the number of heads \(X\) (values \(0,1,2\)) is discrete as the values are countable.
For experiment 2 (rolling a die), the number \(X\) (values \(1,2,3,4,5,6\)) is discrete as the values are countable.
For experiment 3 (listing the set of whole numbers), positive whole numbers \(X\) is discrete as the values are countable.
For experiment 4 (recording basketball scores \(0\leq x\leq25\)), if the scores are counted as whole - number points (e.g., 0,1,2,\(\cdots\),25), \(X\) is discrete. If we consider scores with decimal - like precision (e.g., 10.5 for a free - throw and a field - goal combination in a non - standard counting), it could be continuous. But typically, basketball scores are counted as whole numbers, so \(X\) (scores) is discrete.
For experiment 5 (lifespan of laptop battery), time \(X\) (time until battery becomes defective) is continuous as time can take any value within an interval (e.g., \(t = 1.5\) years, \(t= 2.34\) years).
For experiment 6 (amount of paint to beautify a wall), the amount of paint \(X\) is continuous as it can take any value within an interval (e.g., \(x = 1.2\) liters, \(x = 3.45\) liters).

Answer:

• Discrete: Experiment 1 (tossing a pair of coins), Experiment 2 (rolling a die), Experiment 3 (listing the set of whole numbers), Experiment 4 (recording basketball scores).
• Continuous: Experiment 5 (lifespan of laptop battery), Experiment 6 (amount of paint to beautify a wall).