Pierre Simon Laplace, Inverse Probability, Central Limit Theorem, Probability, Deep Dives.
is ≤ 0.5? To calculate P(p|X_bar_n ≤ 0.5), we need to use a modified version of the formula for inverse probability which uses the incomplete Beta function B(x; a, b) as follows: P(p|X_bar_n ≤ 0.5) using the incomplete Beta function (Image by Author) As before, we set a = x + 1 and b = n — x + 1.