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 Random^Random (Posted on 2014-10-29)
Let A and B each be random real numbers chosen from the uniform interval (0,1).

Call Z the tenths place digit of AB.

Find the probability distribution of Z.

 Submitted by Jer Rating: 5.0000 (1 votes) Solution: (Hide) In general the probability of the first digit being below Z is the integral from 0 to 1 of the function Z/10^(1/X)dX which in closed form is Z/10-ln(Z/10)*Ei(Z/10) Where Ei is the exponential integral function. The approximate distribution: p(Z=0)=.025429 p(Z=1)=.037574 p(Z=2)=.047483 p(Z=3)=.057748 p(Z=4)=.069300 p(Z=5)=.083129 p(Z=6)=.100802 p(Z=7)=.125497 p(Z=8)=.165948 p(Z=9)=.287099

Comments: ( You must be logged in to post comments.)
 Subject Author Date Analytic Solution -- Spolier John Snyder 2015-02-21 09:45:25 re: table of numeric integration Charlie 2014-10-30 08:47:54 re(2): table of numeric integration Charlie 2014-10-30 08:34:08 re(2): table of numeric integration Steve Herman 2014-10-30 08:25:13 re: table of numeric integration Ady TZIDON 2014-10-29 23:13:53 table of numeric integration Charlie 2014-10-29 15:41:37 re: towards an analytic solution - numeric integration Charlie 2014-10-29 15:32:44 towards an analytic solution Charlie 2014-10-29 14:35:18 numerical simulation Charlie 2014-10-29 13:54:25
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