The document discusses binomial probability distributions with N=10 trials, n=5 successes and probability of success p=0.3. It provides the formulas and calculations to find: (a) the probability of exactly 3 successes, P(X=3), (b) the probability of 2 or fewer successes, P(X≤2), (c) the expected value, E(X), and (d) the variance, V(X).

1. Exercice 26
N = 10 n=5 p = 0, 3 = R
N
donc R = 0, 3 × 10 = 3
3 7
C3 · C2 1
(a) P(X = 3) = 10
=
C5 12
(b) P(X ≤ 2)
P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
3 7
C0 · C5 C3 · C7 C3 · C7
= 10
+ 1 10 4 + 2 10 3
C5 C5 C5
1 5 5 11
= + + =
12 12 12 12
(c) E(X ) = n · p = 5 × 0, 3 = 1, 5
(d) V (X ) = N−n
N−1
· n · p · (1 − p) = 5
9
× 5 × 0, 3 × 0, 7 = 7
12