M15: Discrete Probability Distributions

Question 1

Discrete random variable

Answer 1

Finite list of possible outcomes

Question 2

Probability distribution of a discrete random variable

Answer 2

Specify all the values of X and their probabilities
a) Histogram

Question 3

Properties of the probabilities

Answer 3

a) Every probability falls between 0 and 1
b) All probabilities add up to 1

Question 4

Conditions for Binomial Distribution for Count of Successes (BINS)

Answer 4

a) Fixed number of trails n
b) n trials are all independent
c) Outcome = Success/Failure
d) Each trial has the same probability of success, p

Question 5

Parameters of binomial distribution

Answer 5

n / p

Question 6

Independence of Binary Distribution
(Underage drinker problem)

Answer 6

a) No, sample size compared to population
b) No, assumption of independence met

Question 7

Probability of getting exactly x successes out of n trials

Answer 7

(n x) p^x (1-p)^(n-x)

Question 8

Mean of Binomial Distribution

Answer 8

np

Question 9

Standard deviation of Binomial Distribution

Answer 9

sqrt(np(1-p))