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Random variables

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: $X(\omega) = x$, $X(\omega) = y$, $Z(\omega) = x + y$
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Comments

  1. Dieu-Thu LeFebruary 10, 2012 at 12:18 PM

    These equations are indeed ugly~

    ReplyDelete
  2. AnonymousFebruary 10, 2012 at 1:33 PM

    You know you can embed TeX in blogspot right?

    http://watchmath.com/vlog/?p=438

    ReplyDelete
  3. Dieu-Thu LeFebruary 11, 2012 at 12:29 AM

    Yes, I used it..

    ReplyDelete
  4. AnonymousFebruary 11, 2012 at 2:00 AM

    Maybe 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?

    ReplyDelete
  5. Dieu-Thu LeFebruary 11, 2012 at 1:31 PM

    I guess so.. Maybe white background would look better for those equations :)
    Explain? Do you mean those random variables?

    ReplyDelete

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