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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.

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

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Some Thoughts numerical simulation | Comment 1 of 9
The answer should fit this:

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

Private Sub Form_Load()
 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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