--description--

Let $y_0, y_1, y_2, \ldots$ be a sequence of random unsigned 32 bit integers (i.e. $0 ≤ y_i < 2^{32}$, every value equally likely).

For the sequence $x_i$ the following recursion is given:

• $x_0 = 0$ and
• $x_i = x_{i - 1} \mathbf{|} y_{i - 1}$, for $i > 0$. ($\mathbf{|}$ is the bitwise-OR operator)

It can be seen that eventually there will be an index $N$ such that $x_i = 2^{32} - 1$ (a bit-pattern of all ones) for all $i ≥ N$.

Find the expected value of $N$. Give your answer rounded to 10 digits after the decimal point.

--hints--

bitwiseOrOnRandomIntegers() should return 6.3551758451.

assert.strictEqual(bitwiseOrOnRandomIntegers(), 6.3551758451);

--seed--

--seed-contents--

function bitwiseOrOnRandomIntegers() {

  return true;
}

bitwiseOrOnRandomIntegers();

--solutions--

// solution required