Generating random integers >0 that have an expected average value of a given float that is >0

I'm attempting to generate random integers that have an expected value of a given float value. Below are some acceptable distributions:

Expected value: 0.7
Random integers: 0, 1, 0, 1, 1, 1, 1, 0, 1, 1

Expected value: 0.1
Random integers: 0, 1, 0, 0, 0, 0, 0, 0, 0, 0

Expected value: 2.5
Random integers: 2, 2, 2, 3, 2, 3, 3, 3, 2, 3