# Normalizing constant & rejection sampling

I think I understand what a normalizing constant is. Say for example you have a pdf $f(x)$ with support $0 \le x \le 5$. If you wanted to truncate the pdf and only look at $0 \le x \le 3$ you would need to use a normalizing constant $c$ such that $\int_0^3 cf(x)\,dx = 1$.

The problem I'm dealing with states:

In class we gave a rejection method for the case when the target distribution π(x) is only known up to a normalizing constant. Show that the accepted samples from that algorithm indeed follow the target distribution π(x)

What does it mean when it says we only know the target distribution up to a normalizing constant?

Re: What does it mean when it says we only know the target distribution [π(x)] up to a normalizing constant?

This means that π(x) is proportional to the p.d.f. for every value x. That is, if f(x) is the p.d.f., then there is some constant K such that

f(x) = K * π(x)

for all values of x.