Pierre Simon Laplace, Inverse Probability, Central Limit Theorem, Probability, Deep Dives.
the unknown population mean μ (Image by Author) Next, we pair up the blue term on the L.H.S. with the blue term on the R.H.S., and ditto for the yellow terms. Doing us yields the formulae for P(μ|X_bar_n ≤ μ_high) and P(μ|X_bar_n ≤ μ_low) as follows: μ_low and μ_high expressed as inverse CDFs of