General Beta distribution with in arbitrary limits?

I want to generate Beta Random numbers in interval 2 to 5; I want it to have parameters alpha = 3; and beta=2; and I want it to have a variance = 0.33; How do I do it? I know mean is 1/(1+2/3) =3/5 = 0.6 for interval 0 to 1. Rest I have no clue. Thanks in advance.

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Thanks.answers my question completely. A very useful compilation of all distributions and how to generate random numbers from those distributions.
Does this also allow to determine the probability densities of data points under the assumption of a beta distribution with another domain than 0,1? I.e. is there a function like betapdf() for other domains? Thanks in advance
Use a linear transformation of the 0,1 random variables to get them into whatever new range you want, i.e., y = a + b*beta01, where you choose a & b to get the desired new domain.

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