Generate binomial matrix and column-normalize

Using Python with NumPy, generate a $100 \times 100$ matrix of draws from a Binomial distribution with $n = 10$ and $p = 0.3$, using a fixed random seed. Then normalize each column so that it sums to $1$.

Requirements:

• The code must be vectorized.
• Guard against any column that is all zeros: either leave such a column as all zeros, or replace it with a uniform distribution. State which choice you made.
• Verify numerically that the column sums are $1$ within floating-point tolerance.
• Give the time and space complexity of your solution.
• Provide a brief unit test.