# Beta distribution with support from 0 to 2

Is there a way to make the Beta distribution have support from 0 to 2, instead of 0 to 1?

• $$C'(x,\alpha, \beta) = C(x/2, \alpha, \beta)$$
• $$P'(x,\alpha,\beta) = P(x/2,\alpha,\beta)/2$$
where $$C$$ and $$P$$ are the original Beta CDF and PDF and $$C'$$ and $$P'$$ are the new ones (and $$\alpha$$ and $$\beta$$ are the two shape parameters).