Chapter 6

Question 1

What is a probability distribution?

Answer 1

Fully describes the probability of any outcome in the same space.

Question 2

What is a random variable?

Answer 2

A variable whose value depends on the outcome of a random event.

Question 3

What does it mean if a variable is discrete?

Answer 3

It can only take certain numerical values.

Question 4

What does it mean if a variable is random?

Answer 4

The outcome is not known until the experiment is carried out.

Question 5

What is a discrete uniform distribution?

Answer 5

When all the probabilities of different outcomes in an experiment are the same (rolling a fair dice).

Question 6

What does the sum of all the probabilities of all outcomes of an event add up to?

Answer 6

1

Question 7

What is a probability mass function?

Answer 7

f(x) = P(X=x) = (some probability)
x = (certain values)
(When there are different probabilities for x it uses wiggly brackets. It’s just a way of presenting the probability data).

Question 8

What would the probability mass function of a fair 6-sided dice look like?

Answer 8

P(X=x) = 1/6
x = 1,2,3,4,5,6

Question 9

What is a cumulative probability?

Answer 9

The sum of the probabilities of all outcomes up to a particular value.
P(X ≤ x)

Question 10

what is P(X ≥ x) in the form P(X ≤ x)?

Answer 10

P(X ≥ x) = 1 - P(X < x) = 1 - P(X ≤ x-1)

Question 11

What is P(X < x) in the form P(X ≤ x)?

Answer 11

P(X < x) = P(X ≤ x-1)

Question 12

wat is P(X > x) in the form P(X ≤ x)?

Answer 12

P(X > x) = 1- P(X ≤ x)

Question 13

how would you work out P( x ≤ X ≤ y)

Answer 13

= P(X ≤ y) - P(X ≤ x-1)

Question 14

What is the formula for the binomial distribution? in terms of X ~ B(n, p)

Answer 14

P(X = r) = (ⁿCᵣ)pʳ (1- p)ⁿ⁻ʳ
n = number of trials
r = successful outcomes
p = probability of success