# Using probability distributions and variances to modify a formula

We have a lamp and it is in 2m distance. Its light intensity is 5. We want to know what amount of light is reaching to us. We can simply use a formula like: $\mathrm{light} = \frac{\mathrm{intensity}}{\mathrm{distance}}$.

Now suppose that the distance is a random variable (i.e. it is in $2m \pm 1m$ distance, and the intensity is $5 \pm 4.7$).

How we can change the formula in order to be able to use it in case we have random variables too?

P.S. Actually the question is how we can make use of probability distributions, variance, etc. to change the formula?

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I would guess that the denominator should be squared unless something coherent is going on... –  copper.hat Jul 6 '12 at 21:03
can't we work and make use of probability distributions here? –  AKH Jul 6 '12 at 21:07
And there is no need to use three exclamation points! There was a time when typing an exclamation point required 3 keystrokes: you typed a vertical bar, a backspace, and then a period. That made people be somewhat parsimonious with their use. Maybe we should ask that anybody under a certain age be forced to use five or six keystrokes before typing one? –  Arturo Magidin Jul 6 '12 at 21:08
@ArturoMagidin: believe me, people of all ages are prone to this particular phenomenon!! –  Ben Millwood Jul 6 '12 at 21:10
@Ben: And yet, it seems to infect the young more; multiple exclamation points, multiple question marks... Sigh. –  Arturo Magidin Jul 6 '12 at 21:13