Question

which of the following random variables are continuous variables and which are discrete? a) amount of electricity to power a 3 - bedroom home discrete continuous b) number of books in the college bookstore discrete continuous c) number of lightning strikes in rocky mountain national park on a given day continuous discrete d) number of pair of shoes you own discrete continuous e) number of pets you have discrete continuous

Explanation:

Step1: Recall discrete - continuous def

Discrete variables take on countable values. Continuous variables can take on any value in an interval.

Step2: Analyze amount of electricity

The amount of electricity can take on any value within a range (e.g., 10.5 kWh, 10.51 kWh), so it is continuous.

Step3: Analyze number of books

The number of books can only be whole numbers (0, 1, 2, ...), so it is discrete.

Step4: Analyze number of lightning strikes

The number of lightning strikes can only be whole numbers (0, 1, 2, ...), so it is discrete.

Step5: Analyze number of pairs of shoes

The number of pairs of shoes can only be whole numbers (0, 1, 2, ...), so it is discrete.

Step6: Analyze number of pets

The number of pets can only be whole numbers (0, 1, 2, ...), so it is discrete.

Answer:

a) continuous
b) discrete
c) discrete
d) discrete
e) discrete