Calculating parameter from prior density

Question

so I am given a prior density of $$(B+1)Bq(1-q)^{B-1}$$ where q is between 0 and 1 as it represents the probability of death. I am told that my prior mean is 0.1 and I am asked to calculate my parameter B for the prior.

I am just wondering what I have to do to calculate the parameter B i.e. the steps I have to take!

Answer 1

Find prior mean and equate it to $0.1$: $$ \mathbb EX=\int_0^1 q\cdot (B+1)B q(1-q)^{B-1}\,dq =0.1. $$