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Random^Random (Posted on 2014-10-29) Difficulty: 5 of 5
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
SolutionAnalytic Solution -- SpolierJohn Snyder2015-02-21 09:45:25
Solutionre: table of numeric integrationCharlie2014-10-30 08:47:54
re(2): table of numeric integrationCharlie2014-10-30 08:34:08
re(2): table of numeric integrationSteve Herman2014-10-30 08:25:13
Questionre: table of numeric integrationAdy TZIDON2014-10-29 23:13:53
Solutiontable of numeric integrationCharlie2014-10-29 15:41:37
Some Thoughtsre: towards an analytic solution - numeric integrationCharlie2014-10-29 15:32:44
Hints/Tipstowards an analytic solutionCharlie2014-10-29 14:35:18
Some Thoughtsnumerical simulationCharlie2014-10-29 13:54:25
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