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SOA Exam Questions And Answers |Latest
2025 | Guaranteed Pass.
Bernoulli Trial - Answer✔An experiment in which there are exactly two possible outcomes
Binomial distribution - Answer✔A random variable X represents the number of successes
observed from the n Bernoulli trials
Binomial Parameters - Answer✔n = number of trials
p = probability of success
q = 1-p
Binomial probability function (f(x)) - Answer✔
E[X] binomial function - Answer✔E[x] = np
var(x) binomial function - Answer✔var(x) = npq
MGF binomial function - Answer✔
Additive property of binomial function - Answer✔Sum of independent binomially distributed
variables each with probability p, has parameters of p and the sum of all n
1|P a g e
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Negative binomial distribution - Answer✔X is the number of failures before r successes in a
series of independent Bernoulli trials
Negative binomial parameters - Answer✔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) - Answer✔f(x) = Pr(X=x) = (r + x - 1)!/x!(r-1)!
* p^r * q^x
Expected value of negative binomial distribution E[X] - Answer✔E[X] = rq/p
Variance of negative binomial distribution var(x) - Answer✔var(x) = rq/p^2
Moment generating function negative binomial distribution - Answer✔Mx(t) = ((1 - qe^t)/p)^-r
Additive property of negative binomial distribution - Answer✔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 - Answer✔The number of failures observed from the series of Bernoulli
trials until the first success occurs
Parameters of geometric distribution - Answer✔p = probability of success
q = 1-p
2|P a g e
SOA Exam Questions And Answers |Latest
2025 | Guaranteed Pass.
Bernoulli Trial - Answer✔An experiment in which there are exactly two possible outcomes
Binomial distribution - Answer✔A random variable X represents the number of successes
observed from the n Bernoulli trials
Binomial Parameters - Answer✔n = number of trials
p = probability of success
q = 1-p
Binomial probability function (f(x)) - Answer✔
E[X] binomial function - Answer✔E[x] = np
var(x) binomial function - Answer✔var(x) = npq
MGF binomial function - Answer✔
Additive property of binomial function - Answer✔Sum of independent binomially distributed
variables each with probability p, has parameters of p and the sum of all n
1|P a g e
, ©BRIGHTSTARS 2025 ALL RIGHTS RESERVED 11:22 AM A+
Negative binomial distribution - Answer✔X is the number of failures before r successes in a
series of independent Bernoulli trials
Negative binomial parameters - Answer✔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) - Answer✔f(x) = Pr(X=x) = (r + x - 1)!/x!(r-1)!
* p^r * q^x
Expected value of negative binomial distribution E[X] - Answer✔E[X] = rq/p
Variance of negative binomial distribution var(x) - Answer✔var(x) = rq/p^2
Moment generating function negative binomial distribution - Answer✔Mx(t) = ((1 - qe^t)/p)^-r
Additive property of negative binomial distribution - Answer✔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 - Answer✔The number of failures observed from the series of Bernoulli
trials until the first success occurs
Parameters of geometric distribution - Answer✔p = probability of success
q = 1-p
2|P a g e
