Discrete Probability Distributions

Question 1

Conditions of Poisson distribution

Answer 1

• events occur randomly, independently, and at a uniform average rate

Question 2

E(X) and Var(X) in a poisson distriution

Answer 2

E(X) = lambda
Var(X) = lambda

Question 3

Bernoulli trial

Answer 3

A random experiment with only two possible outcomes, success or failure.

Question 4

The binomial distribution is a suitable modelling distribution if the following hold:

Answer 4

• each trial has only two possible outcomes, success or failure (bernouli trial)
• n is fixed
• p is fixed throughout all trials
• trials are independent of one another

Question 5

Mean/expectation and variance of a binomial distribution

Answer 5

Mean=np
Variance=npq

Question 6

When can we use a Poisson distribution to approximate the corresponding binomial distribution?

Answer 6

When n is large and p is small

Question 7

What does the random variable Y~Geo(p) represent

Answer 7

The number of independent binomial trials necessary for the first success

Question 8

Formula for P(X=x) for geometric distribution

Answer 8

p(1-p)^x-1

Question 9

E(X) when x is distributed geometrically

Answer 9

1/p

Question 10

Var(X) when X is distributed geometrically

Answer 10

1-p/p^2

Question 11

Discrete uniform probability

Answer 11

Each of a finite number of values has an equal probability of occurence.

Question 12

P(X=x) for discrete uniform distribution

Answer 12

1/n

Question 13

E(X) for discrete uniform distribution

Answer 13

1/2 x (n+1)

Question 14

Var(X) for discrete uniform distribution

Answer 14

1/12 x (n^2 -1)