'**********************************************************************************
'***************    A Namorada disconfiada   **************************************

Sub JoaoJose()
n = 1000000: p = 0.5: Joao = 0
For i = 1 To n
    pare = 0: conta = 0  'Inicio do jogo
    While pare = 0
        conta = conta + 1
        M1 = (Rnd() > p) + 1 'Moeda 1
        M2 = (Rnd() > p) + 1 'Moeda 2
        If (M1 + M2 <> 1) Then pare = 1 'Pára se der 0 ou 2
    Wend
    If conta Mod 2 = 1 Then Joao = Joao + 1 'Verifica se é impar
Next
MsgBox "Estimativa da Probabilidade: " & Joao / n
End Sub

'**********************************************************************************
'***************    Esperança – O dilema do prisioneiro   *************************
'Um bandido é preso em uma cela que contém 3 portas. A primeira porta o leva a um
'túnel que o conduz à propria cela depois de 2 dias de viagem. A segunda porta
'leva-o a um túnel que o conduz à própria cela depois de 4 dias de viagem.
'A terceira porta o conduz à liberdade depois de um dia de viagem. Se assumimos que
'o bandido seleciona as portas 1, 2 e 3 com probabilidades 0.5, 0.3 e 0.2
'respectivamente, qual o número esperado de dias para que alcance a liberdade?
'http://www.fernandohrosa.com.br/br/P/problem/esperanca-o-dilema-do-prisioneiro/
'**********************************************************************************

Sub Prisioneiro()
n = 100000:
p1 = 0.5: p2 = 0.3
dias = 0
For i = 1 To n
    saida = 0: conta = 0  'Inicio do jogo
    While saida = 0
        x = Rnd()
        If x < p1 Then dias = dias + 2                    'porta = 1
        If x > p1 And x < p1 + p2 Then dias = dias + 4    'porta = 2
        If x > p1 + p2 Then dias = dias + 1: saida = 1    'porta = 3

    Wend
Next
MsgBox "Estimativa do tempo médio para saída: " & dias / n
End Sub

'**********************************************************************************
'***************    O problema dos encontros   ************************************
' Suponha que bolas numeradas de 1 a n são colocadas ao acaso em
' caixas, também numeradas de 1 a n. A bola "encontrou" seu lugar correio se foi
' colocada na caixa de mesmo número. Obtenha a probabilidade de todas as bolas
' irem para caixas erradas.

'**********************************************************************************
'**********************************************************************************
'**********************************************************************************
'**********************************************************************************
'**********************************************************************************
'**********************************************************************************
'**********************************************************************************
'**********************************************************************************
'**********************************************************************************
'**********************************************************************************
'**********************************************************************************
'**********************************************************************************
'**********************************************************************************

Sub Teste()
n = 10
lambda = 0.1
Soma = 0
For i = 1 To n
    x = Rnd()
    y = -1 / lambda * Log(1 - x)
    y = (b - a) * x + a
    Soma = Soma + x
Next
MsgBox "Média = " & Soma / n
End Sub


'**********************************************************************************
'**********************************************************************************

Sub Conjunta()
n = 1000000
Soma1 = 0
Soma2 = 0

For i = 1 To n
    x = 10 * Rnd()
    y = 10 * Rnd()
    fxy = Exp(-(x + y))
    Soma1 = Soma1 + fxy
    If (x < 1 And y > 1 And y < 2) Then Soma2 = Soma2 + fxy
  
Next
MsgBox "Probabilidade = " & Soma2 / Soma1

End Sub


'**********************************************************************************
'**********************************************************************************

Sub FreqInt()
Dim F(20, 2) As Single
Dim y As Double


' K = InputBox("Introduza o Número de classes:")
K = 20
n = 10000
Pi = 4 * Atn(1)

For j = 1 To K
    F(j, 1) = Cells(j + 1, 2)
    ' MsgBox "F(" & i & " , " & 1 & ") = " & F(i, 1)
Next

For i = 1 To n
    'y = Rnd() * 4 - 2  ' Gerando U(-2,2)
    
    R1 = Rnd()
    R2 = Rnd()
    y = Sin(2 * Pi * R1) * Sqr(-2 * Log(R2)) 'Gerando N(0,1)

    'y = Application.NormSInv(Rnd())
    
    For j = 1 To K
        If (y < F(j, 1)) Then F(j, 2) = F(j, 2) + 1
    Next
Next

For j = 1 To K
    Cells(j + 1, 3) = (F(j, 2) - F(j - 1, 2)) / n
Next

' Geração de Gráfico
    ActiveSheet.Shapes.AddChart.Select
    ActiveChart.ChartType = xlXYScatter
    ActiveChart.SetSourceData Source:=Range("B2:C21")
    ActiveChart.SeriesCollection(1).Select
    'ActiveSheet.ChartObjects("Gráfico 1").Activate
    'With Selection
    '    .MarkerStyle = 2
    '    .MarkerSize = 7
    'End With
    'Selection.MarkerStyle = 8
    'Selection.MarkerSize = 6
    'Selection.MarkerSize = 5



'MsgBox "Concluído!"
End Sub


'**********************************************************************************
'**********************************************************************************

Sub SomaNormais()
n = 100000
Pi = 4 * Atn(1)
Soma = 0
For i = 1 To n / 2
    x = Rnd()
    y = Rnd()
    Z = Sqr(-2 * Log(x)) * Cos(2 * Pi * y)
    w = Sqr(-2 * Log(x)) * Sin(2 * Pi * y)
    Soma = Soma + Z + w
Next
MsgBox "Média = " & Soma / n
End Sub

 
'**********************************************************************************
'**********************************************************************************

Sub Constante6()
n = 1000000
Soma1 = 0
Soma2 = 0

For i = 1 To n
    x = Rnd()
    y = Rnd()
    fxy = 1
    Soma1 = Soma1 + fxy
    If (y > x ^ 2 And y < x) Then Soma2 = Soma2 + fxy
  
Next
MsgBox "Constante = " & Soma2 / Soma1

End Sub

 
'**********************************************************************************
'**********************************************************************************

Sub Exemploxxx()
n = 1000000
Soma1 = 0
Soma2 = 0
For i = 1 To n
    x = Rnd()
    y = 2 * Rnd()
    fxy = x ^ 2 + x * y / 3
    Soma1 = Soma1 + fxy
    If (x + y > 1) Then Soma2 = Soma2 + fxy
Next
MsgBox "Probabilidade = " & Soma2 / Soma1
End Sub