SOA EXAM P QUESTIONS AND ANSWERS

SOA EXAM P QUESTIONS AND
ANSWERS

Bernoulli Trial - Correct Answers -An experiment in which there are exactly two possible
outcomes

Binomial distribution - Correct Answers -A random variable X represents the number of
successes observed from the n Bernoulli trials

Binomial Parameters - Correct Answers -n = number of trials
p = probability of success
q = 1-p




Binomial probability function (f(x)) - Correct Answers -

E[X] binomial function - Correct Answers -E[x] = np

var(x) binomial function - Correct Answers -var(x) = npq




MGF binomial function - Correct Answers -

, Additive property of binomial function - Correct Answers -Sum of independent binomially
distributed variables each with probability p, has parameters of p and the sum of all n

Negative binomial distribution - Correct Answers -X is the number of failures before r
successes in a series of independent Bernoulli trials

Negative binomial parameters - Correct Answers -r = desired number of successes
x = number of failures before r successes
p = probability of success
q = 1-p, probability of failure

Negative binomial probability density function f(x) - Correct Answers -f(x) = Pr(X=x) = (r
+ x - 1)!/x!(r-1)! * p^r * q^x

Expected value of negative binomial distribution E[X] - Correct Answers -E[X] = rq/p

Variance of negative binomial distribution var(x) - Correct Answers -var(x) = rq/p^2

Moment generating function negative binomial distribution - Correct Answers -Mx(t) =
((1 - qe^t)/p)^-r
Variance of poisson distribution - Correct Answers -λ

MGF of poisson distribution - Correct Answers -Mx(t) = e^(λ((e^t)-1))

Additive property of poisson distribution - Correct Answers -Sum of poisson distributions
has parameter of the sum of all the λ

Additive property of negative binomial distribution - Correct Answers -If Xi follows a
negative binomial distribution with parameters ri and p, and they are independent, then
the sum of them follows a negative binomial distribution with parameters as the sum of
the ri and p.

Geometric distribution - Correct Answers -The number of failures observed from the
series of Bernoulli trials until the first success occurs

Parameters of geometric distribution - Correct Answers -p = probability of success
q = 1-p
x = number of trials before first success

Probability density function of geometric distribution - Correct Answers -f(x) = Pr(X=x) =
q^x * p

Probability mass function of geometric distribution - Correct Answers -F(x) = Pr(X <= x)
= 1 - q^x+1

Expected value of geometric distribution - Correct Answers -E[x] = q/p