9 votes
Accepted

How to prove, without the LOTUS formula, to student that $V[aX+b]= a^2 V[X]$?

I think you will want to start by convincing the audience that $p(aX+b = ax_i + b)$ is equal to $p(X=x_i)$, probably with examples. I am not an expert statistician so please let me know politely if I ...
Chris Cunningham's user avatar
8 votes

How to prove, without the LOTUS formula, to student that $V[aX+b]= a^2 V[X]$?

This is a consequence of the definition of the variance (1) the linearity of expectation (2) and an algebraic manipulation (3): $$V(aX+b)\stackrel{(1)}{=}\mathbb{E}(aX+b-\mathbb{E}(aX+b))^2\stackrel{(...
Kostya_I's user avatar
  • 1,382
3 votes

How to prove, without the LOTUS formula, to student that $V[aX+b]= a^2 V[X]$?

Do it in two easy steps: Prove that $V[X+b]=V[X]$. This one is easy to prove since variance is a measure of deviation from the mean, hence change of origin will not affect it. Mathematically, $ E({X+...
whoisit's user avatar
  • 131
2 votes

What female mathematician can I introduce to my High School students?

Eugenia Cheng is an important researcher in category theory, and she has published two very good books on popularisation of mathematics with a special touch of 'categorical thinking' - "Cakes, ...
ac15's user avatar
  • 477
1 vote

Math textbook for secondary school using Logo like syntax

I don't know much about math textbooks, but turtle logo is still around from the Python Foundation. Python is often used as a first language because it allows students to start programming with ...
Ben I.'s user avatar
  • 361

Only top scored, non community-wiki answers of a minimum length are eligible