Math Probability Formulae

Question 1

P(A Inter B)
-Independent Case
-Dependent Case

Answer 1

P(A inter B) = P(A) * P(B)
P(A inter B) = P(A) * P(A|B)

Question 2

P(A U B)

Answer 2

P(A U B) = P(A) + P(B) - P(A Inter B)

Question 3

P(A|B)

Answer 3

P(A|B) = P(A inter B) / P(B)

Question 4

Prove Binomial Typical Phrase

Answer 4

soit X une variable aleatoire, X compte les success de n epreuves avec 2 issues (Enoncer issues) identiques et independentes (car …) de parametre p (car …). Ainsi X suit une loi binomiale de parametre n et p.

Question 5

If X follows binomial law then :

Answer 5

P(X = k) = (n k) * p^k * (1-p)^n-k

Question 6

Expected Value formula

Answer 6

E(X) = n*p

Question 7

Variance formula

Answer 7

V(X) = np(1-p)

Question 8

combinatory calculation formula :

Answer 8

n! / k!(n-k)!

Question 9

Check if fluctuation interval exists

Answer 9

P(X E I) = P(a<=X<=b) >= 1 - alpha

Question 10

Check if fluctuation interval is centered

Answer 10

P(X < a) <= alpha/2
P(X > b) <= alpha/2