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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.

 See The Solution Submitted by Jer Rating: 5.0000 (1 votes)

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 numerical simulation | Comment 1 of 9

Three sets of randomized trials are as follows:

Z  probability
0 0.0258100
1 0.0384200
2 0.0466800
3 0.0579100
4 0.0712300
5 0.0832800
6 0.1005900
7 0.1234000
8 0.1664400
9 0.2862400

0 0.0252700
1 0.0382500
2 0.0468700
3 0.0582500
4 0.0694800
5 0.0838100
6 0.1010700
7 0.1273600
8 0.1650100
9 0.2846300

0 0.0257200
1 0.0378300
2 0.0473800
3 0.0572500
4 0.0689100
5 0.0813900
6 0.1029900
7 0.1246100
8 0.1665400
9 0.2873800

Each of these sets is based on 100,000 random pairs of A and B.

from

DefDbl A-Z
Dim crlf\$
Function mform\$(x, t\$)
a\$ = Format\$(x, t\$)
If Len(a\$) < Len(t\$) Then a\$ = Space\$(Len(t\$) - Len(a\$)) & a\$
mform\$ = a\$
End Function

ChDir "C:\Program Files (x86)\DevStudio\VB\projects\flooble"
Text1.Text = ""
crlf\$ = Chr(13) + Chr(10)
Form1.Visible = True
DoEvents

For overtrial = 1 To 3
Randomize Timer
ReDim digCt(9)
For trial = 1 To 100000
b = Rnd(1): x = Rnd(1)
p = b ^ x
ps = mform(p, "0.000000000")
' Text1.Text = Text1.Text & p & crlf
' DoEvents
d = Val(Mid(ps, 3, 1))
'  Text1.Text = Text1.Text & p & "   " & d & crlf
'  DoEvents
digCt(d) = digCt(d) + 1
Next trial
For i = 0 To 9
Text1.Text = Text1.Text & i & mform(digCt(i) / (trial - 1), " 0.0000000") & crlf
Next
DoEvents
Text1.Text = Text1.Text & crlf
Next overtrial

Text1.Text = Text1.Text & crlf & "done"
End Sub

 Posted by Charlie on 2014-10-29 13:54:25

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