Formulari de probabilitat i estadística

$P(\bar{A}) = 1 - P(A)$

$P(A \cup B) = P(A) + P(B) - P(A \cap B)$

$P(A \mid B) = \dfrac{P(A \cap B)}{P(B)}$

$P(A \cap B) = P(B) \cdot P(A \mid B)$

$P(A \cap B) = P(A) \cdot P(B)$

$P(B) = \sum P(A_i)\,P(B \mid A_i)$

$P(A_i \mid B) = \dfrac{P(A_i)P(B\mid A_i)}{\sum P(A_j)P(B\mid A_j)}$

$X \sim B(n, p)$

$P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}$

$\mu = np$

$\sigma^2 = npq$

$\sigma = \sqrt{npq}$

$X \sim N(\mu, \sigma)$

$Z = \dfrac{X - \mu}{\sigma}$

$P(Z \ge a) = 1 - P(Z \le a)$

$P(Z \le -a) = 1 - P(Z \le a)$

$P(a \le Z \le b) = P(Z\le b) - P(Z \le a)$

si $np > 5$ i $nq > 5$: $N(np, \sqrt{npq})$

$\bar{x} \pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}$

$E = z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}$

$n \ge \left(\dfrac{z_{\alpha/2}\,\sigma}{E}\right)^2$

$z = 1{,}645$

$z = 1{,}96$

$z = 2{,}576$