Question

The dispenser for a certain medication can hold up to 5 units, which are dispensed one unit at time upon demand. The demand for this particular medication, however, varies throughout the day, with some days more requests being made than others. Assume that the dispenser is restocked once a day, and any units of medication above the 5 will have to be special ordered. Define a random variable that denotes the number of units of this medication that are withdrawn from the dispenser on any one day. State whether this random variable is discrete or continuous and define the sample space (i.e. range of possible values) for the random variable.

Answer 1

The dispenser for a certain medication can hold upto 5 units, which are dispensed one unit at a time upon demand.

The demand for this particular medication however varies throughout the day, with some days more requests being made than others.

The dispenser is restocked once a day.

Any units of medication above the 5 would have to be specially ordered.

We define a random variable that denotes the number of units of medication that are withdrawn on any day.

Now, this random variable is a DISCRETE variable, because the number of units of medication can be counted like 1,2,3,4 and 5.

The range of this random variable, ie. the sample space is {0,1,2,3,4,5}.