Topic 1: Probability

Question 1

What are 2 properties of basic/elementary events (2)

Answer 1

All basic/elementary events are:
-Mutually exclusive (no 2 can occur at once)
-Mutually exhaustive (at least 1 has to happen)

Question 2

What are the conditions for p(A) being a probability (4)

Answer 2

-Let P be a function whic assigns a real number p(A) to A
-P(A) ≥ 0
-If c_i n c_j = ∅ for I ≠ j, p(c₁ + c₂) = p(c₁) + p(c₂)
-p(Ω) = 1

Question 3

What is bayes theroem (2,1)

Answer 3

-P(A|B) = P(B|A)XP(A)/P(B)
-The posterior = the likelihood x the prior / the marginal

-This is true since P(A|B) = P(AnB)/P(B), and P(B|A) = P(AnB)/P(A)

Question 4

What is relative risk + formula (2,1)

Answer 4

-Relative risk is trying to compare the relative risk of the same event to different groups
-This is the ratio of probabilities

-P(A|Group 1)/P(A|Group 2)

Question 5

How do you calculate the odds ratio (1,1)

Answer 5

-(P(A|Group 1)/P(Ā|Group 1)) / (P(A|Group 2)/P(Ā|Group 2))

-Similar to the relative risk, but including chance of event not happening for groups

Question 6

What is the difference between a combinations and permutations problem (2)

Answer 6

-A combinations problem is a number of ways of selecting a subset of the population without caring about the order
-For a permutations problem, you care about the order

Question 7

What are examples of permutation vs combination problems (2,1)

Answer 7

Permutation:
-If there are n objects to be arranged in order, there are n! ways of doing this
-If there are n objects, you chose ‘r’ of these then order them, there are (n!)/(n-r)! ways

Combinations:
-If there are n objects, you choose ‘r’ of them without ordering you can choose (n!)/r!(n-r)! ways (nCr = nPr/r!, nPr = how many times you can get a certain subset of the population, r! = how many times you can mess up the order)