WEEK 3: Discovering Possibilities and Recognising Patterns

Question 1

Deductive reasoning:

Answer 1

Drawing conclusions from rules you know are true.

E.G Flipping a coin has a 50/50 chance of heads or tail

Question 2

Inductive reasoning:

Answer 2

Look at a small sample to extrapolate the general case (often result in assumptions being used)

E.G Each time the coin is flipped it was heads, thus the next one should be heads.

Question 3

Abductive reasoning:

Answer 3

Also refered to as Occam’s razor: a problem-solving principle that states that the simplest explanation is usually the best

E.G There may be other answers, but “Cheese” was the most obvious one that occurred to you.

Question 4

Context for our decisions:

Answer 4

1. We have limited resources i.e time and money
2. We will have uncertainty in our decisions (very rare to have full information)
3. Statistics is the science of uncertainty & variability

Question 5

Statistics including random and expected variables + variance.

Answer 5

Random variable: A variable that behaves randomly (i.e. we don’t know its value with complete certainty).

Expected variable: In probability, the Expected Value of a random variable is its long-run average value.

Variance: meaning it is a measure of how far a set of numbers is spread out from their average value
Var is calculated by 𝑉𝑎𝑟 = 𝑝 (1 − p)

Independence: If knowing information about one has no impact on the value of the other

Note: When breaking down a problem, try to put it into proportions.
Example: 1 in 5 people are hired therefore 20% chance of an applicant being hired.
Although its a random variable due to us using inductive reasoning
Expected value would be 0.2 tho

Question 6

The normal distribution

Answer 6

Probability distribution: When a pattern occurs often enough and gets studied
- Used to help us find patterns in random variables

Normal distribution: A different pattern that shows up in many different places.
- Defined by the mean and standard deviation