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See an advanced static proof point.

This page uses graduate-level math as a fixed static proof point. SnapCalcAI is not limited to math, and this demo does not upload images or run live solving.

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Static Demo Example

Given X₁,...,Xₙ ~ N(μ, Σ), find the MLE of μ and Σ.

The example turns a dense graduate-level math problem into OCR text, an answer, and structured display pages. It is a high-difficulty example, not the full product range.

This is a static demo preview for the website MVP. It does not require live AI solving in V1.

Original question

Given X₁,...,Xₙ ~ N(μ, Σ), find the MLE of μ and Σ.

OCR text

X₁,...,Xₙ ~ N(μ, Σ)

Answer

μ̂ = x̄; Σ̂ = 1/n Σᵢ(xᵢ − x̄)(xᵢ − x̄)ᵀ

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Display pages
  1. Problem: find the MLE of μ and Σ.
  2. Answer: μ̂ = x̄ and Σ̂ = 1/n Σᵢ(xᵢ − x̄)(xᵢ − x̄)ᵀ.
  3. Step 1: write the Gaussian log-likelihood.
  4. Step 2: set ∂ℓ/∂μ = 0.
  5. Step 3: set ∂ℓ/∂Σ = 0.
Device screen preview
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Problem

Given X₁,...,Xₙ ~ N(μ, Σ),

find the MLE of μ and Σ.

2/5WiFi26%CHG

Answer

μ̂ = x̄

Σ̂ = 1/n Σᵢ(xᵢ − x̄)(xᵢ − x̄)ᵀ

3/5WiFi26%CHG

Step 1

Write the log-likelihood:

ℓ(μ,Σ) = −n/2 log|Σ|

−1/2 Σᵢ qᵢ

This is a static demo preview for the website MVP. It does not require live AI solving in V1.