WEEK 4

Question 1

Partitions

Answer 1

the act of dividing something into separate parts or sections

Question 2

Bayes law

Answer 2

a particular approach to applying probability to statistical problems

Bayes’ Law helps you reverse conditional probabilities — like going from:

“What’s the probability of recovering given you were in surgery?”

to:

“What’s the probability you were in surgery given you recovered?”

P(A|B) = P(B|A)∙P(A) / P(B)

Question 3

Law of total probability

Answer 3

The overall probability of an event happening

P(A) = ∑P(A∩Bₙ)

Question 4

Random variable

Answer 4

any outcomes from some chance process (e.g. rolling a dice)

P(X) = n/N
n = favourable outcomes
N = total possible outcomes

Question 5

Probability distribution

Answer 5

a mathematical function that describes the probability of different possible values of a variable
P(X = x)

Question 6

The two types of probability models

Answer 6

Discrete: probability mass function
Continuous: probability density function

Question 7

What is a probability model ?

Answer 7

A probability model is a mathematical formula that defines the distribution of probabilities for a numerical variable

Question 8

How does the probability mass function differ from the probability density function?

Answer 8

Probability mass function:
- uses discrete random values
- gives an exact probability for each outcome
- probabilities add up to 1
- EXAMPLE: rolling a 3 on a 6-sided die where:
P(X = 3) = 1/6

Probability density function:
- uses continuous random variables
- tells you how dense the probability is at a point
- Can’t give a exact probability for one value; rather, it gives the probability over an interval
- Probabilities are under a curve; the curve’s area = 1
- P(X = a) = 0 at any exact point
- EXAMPLE: heights of people, specifically the interval under 160-170cm
P(160≤X≤170)=areaundercurvebetween160cmand170cm