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Marquer M individus

Recapturer n individus

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$N\approx$

$N\approx$

Quelle est la proportion f des poissons marqués
lors de cette seconde capture ?

f=

Estimer le nombre total N d'individus.

Non... Essaye encore. 
On estime que $\frac{n}{N}=f$ donc...

Non... essaye encore. $f=\frac{k}{K}$

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Réponse

Réponse

\text{Si } \frac{M}{N}=\frac{m}{n} \text{ alors :  } N=M\times\frac{n}{m}

Ntest2 = 0
Ntest1 = 0
t = 0 (slider from 0 to 1, step 0.01)
p = false
Nbpoissons: Random[500, 900] + p
N: Nbpoissons
LaleaN2 = Sequence(Random[0, 500] / 100, k, 1, (2 * N))
LPN2 = Sequence((Element[LaleaN2, k], Element[LaleaN2, (2 * k)]), k, 1, N)
LaleaN = Sequence(Random[0, 500] / 100, k, 1, (2 * N))
LPN = Sequence((Element[LaleaN, k], Element[LaleaN, (2 * k)]), k, 1, N)
LPNt = Sequence(((1 - t) * Element[LPN, k]) + (t * Element[LPN2, k]), k, 1, N)
A = Intersect(xAxis, yAxis)
B = (5, 0)
poly1, f, g, h, i, C, D = Polygon(A, B, 4)
Z = Midpoint(f)
segmax = Segment(A, Z)
H = Point(segmax)
nn = Sum(Sequence[If[x(Element[LPN, k]) ≤ x(H) ∧ y(Element[LPN, k]) ≤ x(H), 1, 0], k, 1, N])
l4 = Sequence(If[Max[x(Element[LPN, k]), y(Element[LPN, k])] < x(H), ((1 - t) * Element[LPN, k]) + (t * Element[LPN2, k])], k, 1, N)
E = Point(segmax)
k = Sum(Sequence[If[x(Element[l4, k]) ≤ x(E) ∧ y(Element[l4, k]) ≤ x(E), 1, 0], k, 1, N])
K = Sum(Sequence[If[x(Element[LPNt, k]) ≤ x(E) ∧ y(Element[LPNt, k]) ≤ x(E), 1, 0], k, 1, N])
fracf: k / K
fracfround: round(fracf, 4)
Nestim1: floor(nn / (fracfround + 0.001)) - 1
Nestim2: floor(nn / (fracfround - 0.001)) + 1
Nestim: floor((K * nn / k))
NOK: Nestim1 ≤ Ntest1 ≤ Nestim2 ∨ Nestim1 ≤ Ntest2 ≤ Nestim2 ∧ Ntest1 ≠ 0
a: Random[0, 500] / 100
l2 = Sort(LPN)
poly2, j, kk, l, m, F, G = Polygon(A, E, 4)
LRecapture = Sequence(If[x(Element[LPNt, k]) ≤ x(E) ∧ y(Element[LPNt, k]) ≤ x(E), Element[LPNt, k]], k, 1, N)
b = false
c = false
poly3, q, r, s, f_1, I, J = Polygon(A, H, 4)
texte6: "" + Nestim + ""
InputBox1 = Textfield(Ntest1)
compterr1 = If(Ntest1 ≠ Nestim ∧ Ntest1 ≠ 0, 1, 0)
InputBox2 = Textfield(Ntest2)
NbParties: 0
NbPartiesGain: 0
fracfTest = 0
InputBox3 = Textfield(fracfTest)
text6: "Oui, prenons $f\approx " + (LaTeX[fracfround]) + "$"
fracOK: fracfTest ≟ fracf ∨ fracfround - 0.015 < fracfTest < fracfround + 0.015
PointsPartie: (NOK + fracOK) / 2
texte4: "En fait il y en avait " + (LaTeX[N]) + ""
compterr0 = If((¬fracOK) ∧ fracfTest ≠ 0, 1, 0)
Nfaux2: (¬NOK) ∧ Ntest2 > Nestim2 ∨ Ntest2 < Nestim1 ∧ Ntest2 ≠ 0
text3: "Score : " + NbPartiesGain + " sur " + NbParties + " "
fmin = Max(fracf - 1 / sqrt(nn), 0)
fmax = Min(fracf + 1 / sqrt(nn), 1)
Nmin: round(nn / fmax, 0)
Nmax: round(nn / fmin, 0)
text12: "Intervalle de confiance à 95% :
Pour f : [ " + fmin + " ; " + fmax + " ]
Pour N : [" + Nmin + " ; " + Nmax + "]"
Nestim0: nn / fracfround
text1: "On peut estimer N à " + Nestim + ""
affrep1 = false
texte1: "M=" + (LaTeX[nn]) + ""
texte2: "n=" + (LaTeX[K]) + ""
text4: "dont $m=" + (LaTeX[k]) + "$ sont marqués."