# Random variable and its support

Q: Cells live for a random but finite amount of time and when they die they leave behind k offspring with probability pk for k=0,1,2. Initially there is one cancer cell in a petri dish. After one hour a scientist counts the number of cancer cells in the petri dish. What is the random variable and its support for this experiment?

My attempt so far is :

Denote by X the random variable equal to the number of cells in the petri dish

Supp(X) = ?

I am not quite sure if it is right but my thoughts leaded me to say {0,1,2}

Any help on this will be highly appreciated

Thanks alot

• Saying that the support is $\{0,1,2\}$ assumes that only one cell death occurs during the course of the hour; an assumption not warranted by the question as asked. – Omnomnomnom Jun 28 '13 at 23:01

## 1 Answer

The random variable being measured in this experiment is the total number of cells in the petri dish after an hour.

We are not given any information about how quickly these cells divide, so given only this information we have no upper limit for how many cells there might be in the dish after an hour, and the cells can divide in such a way that there are any number of them after a given time.

So, the support of this random variable is the non-negative integers, since there can be any number (from $0$ and up) of cells after an hour.