SOA PA Exam Questions With Complete Solutions.

Bernoulli Trial - An experiment in which there are exactly two possible outcomes Binomial distribution - A random variable X represents the number of successes observed from the n Bernoulli trials Binomial Parameters - n = number of trials p = probability of success q = 1-p Binomial probability function (f(x)) - E[X] binomial function - E[x] = np var(x) binomial function - var(x) = npq MGF binomial function - Additive property of binomial function - Sum of independent binomially distributed variables each with probability p, has parameters of p and the sum of all n Negative binomial distribution - X is the number of failures before r successes in a series of independent Bernoulli trials Negative binomial parameters - r = desired number of successes x = number of failures before r successes p = probability of success q = 1-p, probability of failureNegative binomial probability density function f(x) - f(x) = Pr(X=x) = (r + x - 1)!/x!(r-1)! * p^r * q^x