Binomial Distribution

Question 0

What is the variance of the binomial distribution?

Answer 0

variance = npq

where p = probability of success
q = probability of failure
n = number of trials.

Question 1

What is the mean of the binomial distribution?

Answer 1

mean = np

Where p = probability of success and
n = number of trials

Question 2

What is the PMF of the binomial distribution?

Answer 2

P[X=x] = (n C r) (p)^r (q)^n-r

Where n = number of trials
r = number of successes
p = probability of success
q = probability of failure

Question 3

What is a Bernoulli trial?

Answer 3

An experiment with exactly two outcomes: Success or Failure

Question 4

What is a Bernoulli experiment?

Answer 4

A sequence of independent Bernoulli trials?

Question 5

What is a multinomial distribution?

Answer 5

A generalization of the binomial distribution for n independent trials. Each of which leads to success for exactly one of k categories.

Question 6

What is the PMF of the multinomial distribution?

Answer 6

P[X=x] = (n!/r1! * r2! *…rn!) (p1^r1)(p2^r2)…(pn^rn)

Question 7

What are the two forms of the moment generating function of the binomial distribution?

Answer 7

Mx(t) = (1 + p ((e^t) - 1)) ^ n

Mx(t) = (pe^t + (1-p))^n