Actuary Exam 1 Questions & Answers 2023/2024
Mutually Exclusive Outcomes: - ANSWER-Outcomes that cannot occur simultaneously. (disjoint)
Exhaustive Outcomes: - ANSWER-Combine to the entire probability space. Or, one of the outcomes must occur whenever the experiment is performed.
DeMorga...
P[A or B (giv) C] = - ANSWER-P[A(giv)C] + P[B(giv)C] - P[A & B (giv) C]
Given n distinct objects, the number of ways in which the objects may be ordered: - ANSWER-n!
Choosing ordered subset of size k withouth replacement from n objets: - ANSWER-n! / (n-k)! P(n,k)
# of ways of ordering n objects of different types: - ANSWER-n! /( n1! * n2!*.....nt!)
# of ways of choosing a subset without replacement. (no regard to order): - ANSWER-n! / (k! * (n - k)!)
When considering combinations, the order of the elements in the set is: - ANSWER-irrelevant: {a,b} =
{b,a}
When considering permutations, the order is: - ANSWER-important: {a,b} does not equal {b,a}
Random Variable: - ANSWER-function on a probability space S
Discrete Distribution: - ANSWER-Can only take on values from a finite infinite sequence.
Probability Mass: - ANSWER-The probability at a point of a discrete random variable.
Cumulative Distribution Function: - ANSWER-F(x) = P[X<x] (Probability to the left of, and including, the
point x)
Survival Function: - ANSWER-Complement of the Cumulative Distribution Function
For Discrete Random Variable E[X] = - ANSWER-x1*p(x1) + x2*p(x2) + .......
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