# Tag Info

Accepted

• 97.6k
1 vote

### On Definition of Random Variables

To quote from Wikipedia, a $\sigma$-algebra is defined as $\Omega$ is in $\mathcal F$, and $\Omega$ is considered to be the universal set in the following context. $\mathcal F$ is closed under ...
• 92.7k
1 vote
Accepted

As @whoknowsnot has shown, for every $a \in \mathbb R$, the event $\{X< a\}\in \mathcal F$, and since $\{X\leq a\}\in \mathcal F$ by definition, the difference of these two events, namely $\{X = ... 1 vote ### Can two random variables, both of which are dependent on a 3rd random variable, be independent of each other? This is possible. Two examples: Discrete example Throw two coins independently, but code the outcomes as 0 or 1. Then define:$\$ \begin{align} X&=\text{outcome on first coin}\\ Y&...
• 65.8k

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