Probability - Distributions

Question 1

Discrete Random Variable

Answer 1

• discrete if in a countable range

Question 2

Binomial Distribution

Answer 2

Number of successes in a fixed number of independent trials

2 outcomes - success or failure

Question 3

Binomial Expectation

Answer 3

E[x] = np

Question 4

Binomial Variance

Answer 4

Var(x) = np(1-p)

Question 5

Bernoulli Distribution

Answer 5

Discrete Probability Distribution that models a single event - success or failure

Question 6

Bernoulli Expectation

Answer 6

E[x] = p

Question 7

Bernoulli Variance

Answer 7

Var(x) = np

Question 8

Binomial PMF

Answer 8

(n choose p) p^j (1-p)^(n-j)

Question 9

Bernoulli PMF

Answer 9

f(0) = 1-p
f(1) = p

Question 10

Uniform Distribution

Answer 10

each event is equally likely to occur

Question 11

Uniform Expectation

Answer 11

E[x] = (n + 1) / 2

Question 12

Uniform Variance

Answer 12

Var(x) = (n^2 -1) / 12

Question 13

Uniform PMF

Answer 13

f(i) = 1 / n

Question 14

Geometric Distribution

Answer 14

Number of independent Bernoulli trials needed to achieve first success.

Question 15

Geometric Expectation

Answer 15

E[x] = (1-p) / p

Question 16

Geometric Variance

Answer 16

Var(x) = (1-p) / p^2