[R] runif with condition

[Carl Witthoft]

AlanM said,
"Consider the pair {X, 1-X} where X is sampled from a uniform(0,1) 
distribution. The quantity 1- X also comes from a uniform(0,1) 
distribution and therefore is probabilistic and not deterministic. The 
sum of independent random variables is itself a random variable. If X1, 
X2 & X3 are uniformly distributed, then the distribution of Y = X1 + X2 
+ X3 can be determined (i.e. Y is probabilistic and NOT deterministic). 
Y is a random variable, but it is correlated with X1, X2 and X3. The set 
{X1, X2, X3, 100 - (X1 + X2 + X3) } contains 4 random variables, however 
they are neither independent or identically distributed.

  If you are curious, check this out.

Deriving the Probability Density for Sums of Uniform Random Variables 
Edward J. Lusk and Haviland Wright
The American Statistician
Vol. 36, No. 2 (May, 1982), pp. 128-130"
(endquote)


Be *very* careful about how you state the problem.  The quantity (1-X), 
once you know the value of X, is deterministic.  The confusion arises, I 
think, in that if you do NOT know the value of X, then both X and (1-X) 
are unknown and probabilistic.  But, rather like entangled photons :-), 
once you know one of the values, you immediately know the other.

I'll sign off with the reminder that, back when Marylin vos Savant first 
published the Monte Hall problem, a number of people with PhDs in math, 
some of whom claimed to be statisticians, angrily supported the 
incorrect answer.

Carl

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