Discrete probability distributions

Question 1

Conditions for binomial distribution

Answer 1

Fixed number of trials
fixed chance of success
two outcomes only
independent success rate of trials

Question 2

conditions of poisson distribution

Answer 2

mean rate of occurrence in a given time period
random event
events are independent of each other

Question 3

Binomial notation

Answer 3

X ~ B(n, p)
where n is the number of trials and p is the chance of success

Question 4

Binomial formula

Answer 4

P (X = r) = nCr x p^r x q^n-r

Question 5

E(X) for binomial distribution

Answer 5

E(X) = np

Question 6

Var(X) for binomial distribution

Answer 6

Var(X) = npq
or np - np^2

Question 7

poisson formula

Answer 7

P(X = r) = e^-λ x λ^r/r!
where λ = the mean rate of occurrence

Question 8

poisson notation

Answer 8

X ~ Po(λ)
λ i.e mean rate of occurrence

Question 9

poisson skew

Answer 9

positively skewed
has less of an effect as λ increases

Question 10

what is a unique feature of poisson distribution

Answer 10

E(X) = Var(X) = λ
good for questions which ask what type of distribution is appropriate

Question 11

If X ~ Po(x)
and Y ~ Po(y)
Then what is X + Y

Answer 11

X + Y ~ Po(x + y)