I was just shown this website so I really have no clue how things work. Let me know if I do something wrong please. Also, please bare with me because English is not my first language and I'm really bad at Math.
Me and my friend who showed me this website are doing this online course for seniors, and have no base knowledge of most advanced math .. so please bare with me.
Here's one of my first assignment exercises :
Consider a random variable X so that : $\operatorname{E}[(X-1)^2]=10$ and $\operatorname{E}[(X-2)^2]=5$
Please solve :
1 - The expected value of X: $\operatorname{E}[X]$
2 - The variance of X: $\operatorname{V}[X]$
In regards to this, could you please help with some tips of what subject to study (the subject, a book, a website?)
Thanks in advance,
Paulo
Expectation is linear, so $E[(X-1)^2] = E[X^2] - 2 E[X] + 1=10$ and $E[(X-2)^2] = E[X^2 - 4 X +4] = E[X^2] - 4 E[X] +4=5$.
From these two equations, you can solve for $E[X],E[X^2]$. Then, note $var(X) = E[X^2] - (E[X])^2$.