SOA Exam P RV distributions With Correct Answers
Discrete Uniform - Correct Answer a finite number of values consecutively spaced by
1, all of which are equally likely
X ~ Uniform(a,b)
a= smallest possible value
b= largest possible value
PMF of X: uniform distribution - Correct Answer Pr(X=x) = 1/ (b-a+1)
E[X]: uniform distribution - Correct Answer = (a + b) / 2
Var(X): uniform distribution - Correct Answer = ((b - a + 1)^2 - 1) / 12
MGF: uniform distribution - Correct Answer = (e^at - e^(b+1)t) / (1 - e^t)(b-a+1)
Bernoulli Distribution - Correct Answer only 2 possible values: 0 or 1
0 is "failure" with probability 1-p; 1 is "success" with probability p
X ~ Bernoulli(p)
PMF: Bernoulli distribution - Correct Answer Pr(X = x) = { p, x=1
q=1-p, x=0}
E[X]: Bernoulli distribution - Correct Answer = p
Var(X): Bernoulli distribution - Correct Answer = p*q
E[X^2]: Bernoulli distribution - Correct Answer = p
Discrete Uniform - Correct Answer a finite number of values consecutively spaced by
1, all of which are equally likely
X ~ Uniform(a,b)
a= smallest possible value
b= largest possible value
PMF of X: uniform distribution - Correct Answer Pr(X=x) = 1/ (b-a+1)
E[X]: uniform distribution - Correct Answer = (a + b) / 2
Var(X): uniform distribution - Correct Answer = ((b - a + 1)^2 - 1) / 12
MGF: uniform distribution - Correct Answer = (e^at - e^(b+1)t) / (1 - e^t)(b-a+1)
Bernoulli Distribution - Correct Answer only 2 possible values: 0 or 1
0 is "failure" with probability 1-p; 1 is "success" with probability p
X ~ Bernoulli(p)
PMF: Bernoulli distribution - Correct Answer Pr(X = x) = { p, x=1
q=1-p, x=0}
E[X]: Bernoulli distribution - Correct Answer = p
Var(X): Bernoulli distribution - Correct Answer = p*q
E[X^2]: Bernoulli distribution - Correct Answer = p
