(Question from Mathematics for the international student Mathematics SL. Third Edition)

For each of the following:

  1. identify the random variable being considered
  2. give possible values for the random variable
  3. indicate whether the variable is continuous or discrete

 

a) To measure the rainfall over a 24-hour period in Singapore, the height of water collected in a rain gauge (up to 400 mm) is used.

  1. The random variable (X) is the height of water collected in the rain gauge.
  2. Since the rain gauge has a max height of 400 mm, the possible values fall anywhere where $\color{red} 0 \leq X \leq 400$.
  3. Since the height can take on ANY value in the interval 0 to 400, this is a continuous random variable.

 

b) To investigate the stopping distance for a tyre with a new tread pattern, a braking experiment is carried out.

  1. The random variable (X) is the stopping distance.
  2. Not much information is given in this question, so the POSSIBLE values for X is  $0 \leq X $. Obviously, X won’t ever reach 9000 m or anything crazy like that… unless we are on a flat frictionless surface. So  $0 \leq X $ takes into account all of these scenarios.
  3. The stopping distance can take on ANY value, so this is a continuous random variable.

 

c) To check the reliability of a new type of light switch, switches are repeatedly turned off and on until they fail.

  1. The random variable (X) is the number of times the switches are turned on and off until they fail.
  2. The number of times a light switch can be turned on and off can ONLY take on integer numbers (unless you can think of a way to turn on a light switch 1.624 times?). So we have  $1 \leq X $, where X is an integer. Or you can write it as  $1 \leq X, X \in \mathbb{Z}$ . **Nerdy note:  $\mathbb{Z}$  represents integers because it comes from the German “Zahlen”, which means “number”.**
  3. Since it can only take on integers, this is a continuous random variable.