Pierre Simon Laplace, Inverse Probability, Central Limit Theorem, Probability, Deep Dives.
want to find a μ_low and a μ_high such that: P(μ ≤ μ_low) = F(μ_low) = 0.025, and P(μ ≤ μ_high) = F(μ_high) = (1 — 0.025) That is, you’d want to find a μ_low such that the area under the PDF of X from negative ∞ to μ_low is 0.025. This area is the blue region in the figure below. Since we know the