The below program invokes the randomization initialization when the user clicks the start button, which I did 10 times. At 100,000 trials per click, there were a million trials, hopefully better randomized than if one sequence of a million trials were done without interrupting the randomization process at random.
DefDbl A-Z
Dim crlf$, type1, type2, type3, type4, trials
Private Sub Command1_Click()
Randomize Timer
For tr = 1 To 100000
DoEvents
x = 16 * Rnd(1): xdig$ = firstdig$(x)
x3 = x ^ 3: x3dig$ = firstdig$(x3)
threex = 3 ^ x: threexdig$ = firstdig$(threex)
If xdig = threexdig Then type1 = type1 + 1
If xdig = x3dig Then type2 = type2 + 1
If threexdig = x3dig Then type3 = type3 + 1
If xdig = threexdig And xdig = x3dig Then type4 = type4 + 1
trials = trials + 1
Next tr
Text1.Text = Text1.Text & mform(type1 / trials, " 0.0000000000") & mform(type2 / trials, " 0.0000000000")
Text1.Text = Text1.Text & mform(type3 / trials, " 0.0000000000") & mform(type4 / trials, " 0.0000000000") & crlf
End Sub
Private Sub Form_Load()
Form1.Visible = True
Text1.Text = ""
crlf = Chr$(13) + Chr$(10)
x = x
End Sub
Function firstdig$(n)
s$ = hexreal$(n)
For i = 1 To Len(s$)
If InStr("123456789abcdef", Mid(s, i, 1)) > 0 Then Exit For
Next i
firstdig$ = Mid(s, i, 1)
End Function
Function hexreal$(n)
intpart = Int(n)
fracpart = n - intpart
h$ = "."
While intpart > 0
q = Int(intpart / 16)
r = intpart - q * 16
intpart = q
h = Mid("0123456789abcdef", r + 1, 1) + h
Wend
While fracpart > 0
m = fracpart * 16
d = Int(m)
fracpart = m - d
h = h + Mid("0123456789abcdef", d + 1, 1)
Wend
hexreal$ = h
End Function
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
The first row below represents the statistics based on the first 100,000 trials. Each successive row adds in the results of the next 100,000, so that the final row represents the results of a million trials.
0.0447300000 0.0838700000 0.1664200000 0.0102400000
0.0441550000 0.0841100000 0.1658800000 0.0101700000
0.0440300000 0.0847200000 0.1654000000 0.0104800000
0.0439425000 0.0846525000 0.1654300000 0.0105675000
0.0440080000 0.0844860000 0.1653320000 0.0105520000
0.0439966667 0.0844466667 0.1654616667 0.0106216667
0.0439528571 0.0845685714 0.1655300000 0.0105814286
0.0438562500 0.0846700000 0.1655200000 0.0105325000
0.0439455556 0.0847811111 0.1653211111 0.0105255556
0.0438500000 0.0847820000 0.1653790000 0.0105160000
In the final tally 43,850 out of the million trials got a hit for situation (i), 84,782 hit situation (ii), 165,379 hit situation (iii) and 10,516 hit all (iv).
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Posted by Charlie
on 2016-06-19 21:25:11 |
Simulations for all parts
