A random variable is a mapping from a sample space to real numbers $\Omega \rightarrow \mathrm{R}$
At a certain point in most probability courses, we don't see the sample space, but it's always there, lurking in the background.
For example:
Let $\Omega = \{(x,y); x^2 + y^2 \leq 1\}$ be the unit disc. Consider drawing a point "at random" from $\Omega$.
Outcome: $\omega = (x,y)$.
Examples of random variables: $X(\omega) = x$, $X(\omega) = y$, $Z(\omega) = x + y$
At a certain point in most probability courses, we don't see the sample space, but it's always there, lurking in the background.
For example:
Let $\Omega = \{(x,y); x^2 + y^2 \leq 1\}$ be the unit disc. Consider drawing a point "at random" from $\Omega$.
Outcome: $\omega = (x,y)$.
Examples of random variables: $X(\omega) = x$, $X(\omega) = y$, $Z(\omega) = x + y$
These equations are indeed ugly~
ReplyDeleteYou know you can embed TeX in blogspot right?
ReplyDeletehttp://watchmath.com/vlog/?p=438
Yes, I used it..
ReplyDeleteMaybe it has something to with the Pinky background (: and the border styling of the images. Btw, I don't get what you stated here. Care to explain?
ReplyDeleteI guess so.. Maybe white background would look better for those equations :)
ReplyDeleteExplain? Do you mean those random variables?