Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable. (a) The number of hits to a website in a day. (b) The time it takes to fly from City A to City B. (a) Is the number of hits to a website in a day discrete or continuous? A. The random variable is discrete. The possible values are $x=0,1,2, \ldots$. B. The random variable is discrete. The possible values are $x \geq 0$. C. The random variable is continuous. The possible values are $x=0,1,2, \ldots$ D. The random variable is continuous. The possible values are $x \geq 0$. (b) Is the time it takes to fly from City A to City B discrete or continuous? A. The random variable is continuous. The possible values are $t=1,2,3, \ldots$ B. The random variable is discrete. The possible values are $t>0$. C. The random variable is discrete. The possible values are $t=1,2,3, \ldots$ D. The random variable is continuous. The possible values are $t>0$.
Solution
Step 1 ：Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable.
Step 2 ：(a) The number of hits to a website in a day is a countable quantity, which means it can only take on integer values. Therefore, it is a discrete random variable. The possible values it can take are all non-negative integers, starting from 0 (no hits) and going up to any possible number of hits.
Step 3 ：(b) The time it takes to fly from City A to City B is a measurable quantity, which means it can take on any value within a certain range. Therefore, it is a continuous random variable. The possible values it can take are all positive real numbers, starting from 0 (immediate arrival, which is theoretically possible but practically impossible) and going up to any possible duration of time.
Step 4 ：Final Answer: \(\boxed{\text{(a) The random variable is discrete. The possible values are } x=0,1,2, \ldots \text{.}}\)
Step 5 ：Final Answer: \(\boxed{\text{(b) The random variable is continuous. The possible values are } t>0 \text{.}}\)
