The mean is a/(a+b) so if you make a = 0.35 and b = 0.65 then the mean on (0,1) is 0.35. Generate the random numbers from 0 to 1 using beta(0.35,0.65) and multiply them by 10. They will make a cup shaped beta shaped curve from 0 to 10 but the ends will be different heights.

=BETAINV(RAND(),0.35,0.65)*10 in Excel gives this shape.