Python 3 : instructions avancées - Exercices Python 3: advanced instructions - Exercises Python 3: instrucciones avanzadas - Ejercicios

[5, 8, 2, 9] → [5, 8, 2, 9, 4] → [5, 2, 9, 4] → [50, 2, 9, 4].

Affichage : [50, 2, 9, 4] 4

def moyenne(L):
    s = 0
    for x in L:
        s = s + x
    return s / len(L)

print(moyenne([12, 15, 9, 14]))

Le programme affiche 12.5

def maximum(L):
    m = L[0]
    for x in L:
        if x > m:
            m = x
    return m

print(maximum([3, -1, 17, 8]))   # 17

1) et 2)

def f(x):
    return x ** 2 - 4 * x + 1

valeurs = []
for x in range(6):
    valeurs.append(f(x))
    print(f(x))

3)

[1, -2, -3, -2, 1, 6]

def termes(n):
    u = 1
    L = [u]
    for k in range(n):
        u = 2 * u + 1
        L.append(u)
    return L

print(termes(4))

[1, 3, 7, 15, 31]

1)

from random import randint
nb6 = 0
for i in range(1000):
    if randint(1, 6) == 6:
        nb6 = nb6 + 1
print(nb6 / 1000)

2)

Vers $\dfrac{1}{6} \approx 0{,}167$

from random import random
def succes(n, p):
    k = 0
    for i in range(n):
        if random() < p:
            k = k + 1
    return k

print(succes(20, 0.3))

La valeur renvoyée suit la loi $\mathcal{B}(n\,;\,p)$ ; en moyenne elle vaut $np = 6$ ici.

1)

def rectangles(n):
    s = 0
    for k in range(n):
        x = k / n
        s = s + (1 / n) * x ** 2
    return s

2)

$\dfrac{1}{4}\left(0 + \dfrac{1}{16} + \dfrac{4}{16} + \dfrac{9}{16}\right) = \dfrac{14}{64} = 0{,}21875$.

$0{,}21875$ alors que la valeur exacte est $\dfrac{1}{3} \approx 0{,}333$ ; l'approximation s'améliore quand $n$ augmente

from math import exp
from matplotlib.pyplot import *
x = []
y = []
for i in range(50):
    t = 5 * i / 49
    x.append(t)
    y.append(exp(-t))
plot(x, y, color="green", label="y = exp(-x)")
plot([0, 5], [0.5, 0.5], "--", color="red")
legend()
show()

def seuil(A):
    n = 0
    u = 1
    while u >= A:
        u = u * 0.9
        n = n + 1
    return n

print(seuil(0.1))

$0{,}9^n < 0{,}1 \iff n > \dfrac{\ln 0{,}1}{\ln 0{,}9} \approx 21{,}85$.

seuil(0.1) renvoie $22$