On 2014-02-13 14:18, Dan Asimov wrote:
Let e_j, j = 1,2,3,… be independent random variables each taking the values +-1 with probability 1/2.
Let the random variable X be defined as
X := Sum_{n=1…oo} e_j/2^j.
PUZZLE: What is the distribution of X ???
—Dan _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
. . . . . . . . If I have a uniformly distributed number between 0 and 1, expressed in binary, I would assume that the probability is .5 that any particular bit was a 1. Now, if I subtract .5 from each bit, the value of the number decreases by .5, so now uniform between -.5 and +.5 (and each bit is randomly +-.5) Finally, I multiply by 2, so uniform between -1 and 1 (and each bit is randomly +-1). Seems like a round about way of getting there, but requiring about as much thought as I'm capable of while coding.