# 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

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.