MethodMath Math Questions and Answers

I am studying probability theory and I need to understand moment generating functions (MGFs). The MGF of a random variable $X$ is:

My questions:

1. Why is it called

I have a trig final next week and Im drowning in identities.

Theres like 50 of them:

• Pythagorean identities
• Angle addition formulas
• Double angle formulas
• Half

I am studying graph theory and I keep confusing Eulerian paths with Hamiltonian paths. Can someone clarify the difference?

Eulerian path: A path that uses every edge exactly once.
**Hamiltonian

Another viral math meme:

People are arguing because:

• If you do $230 - 220 = 10$, then $10 \times 0.5 = 5$ ✓
• But PEMDAS says multiplication first: $220 \times 0.5 = 110$, then $230 - 110 = 120$.

So

I'm studying probability and I understand the formula for Bayes' Theorem:

But I struggle to understand when to apply it. The theorem feels backwards somehow — we are using

I need to understand the simplex algorithm for solving linear programming problems.

Consider the problem:

Maximize $z = 3x_1 + 2x_2$
Subject to:

Can someone walk through the steps:

1. Convert

I heard about Hilberts hotel. The one with infinitely many rooms thats always full but can always take more guests.

If the hotel is full and 1 more person shows

I am studying combinatorics and I am fascinated by Catalan numbers. The $n$-th Catalan number is:

The first few are: 1, 1, 2, 5, 14, 42, 132, 429,