Exam P Review Sheet北美精算师资格考试试题 精算师考试复习资料.pdf

Exam P Review Sheet x k ln(y) log (b ) = x log (y ) = k log (y) log (y) = b b b b ln(b) log (yz) = log (y) + log (z) log (y/z) = log (y) − log (z) b b b b b b x ln(y) ln(e ) = x e = y for y 0. d x x x ax dx a = a ln(a) a dx = ln(a) for a 0. ∞ xn e−cxdx = n! . In particular, for a 0, ∞ e−atdt = 1 0 cn+1 0 a 1 − rn+1 rn+1 − 1 2 3 n a + ar + ar + ar + · · · + ar = a = a 1 − r r − 1 a if |r | 1 then a + ar + ar2 + ar3 + · · · = ∞ ari = i=0 1 − r a Note: (derivative of above) a + 2ar + 3ar2 + · · · = 2 . (1 − r) If A ⊆ B , then P (A) ≤ P (B). P (A ∪ B) = P (A) + P (B) − P (A ∩ B) P (A) = P (A ∩ B) + P (A ∩ B ) P (A ∩ B) If P (A) 0, then P (B |A) = , and P (A ∩ B) = P (B |A)P (A). P (A) P (B) = P (B |A)P (A) + P (B |A )P (A ) (Law of Total Probability) P (B |A)P (A) P (A |B) = (Bayes)