Probability Flashcards
Why would s.d be preferred to variance?
> often the translation of unit meanings in variance is lost as many units cannot be squared (time etc.)
therefore s.d is easier to interpret and apply.
Types of probability
- Theoretical
- Empirical
- Judgemental
theoretical probability
a mathematical description
Empirical/experimental probability
based on data from an experiment (observation)
Judgemental/subjective probability
Used when calculating either theoretical or empirical probability is not possible
> based on expert opinion
Intersection
> probability that both A and B occur
A ∩ B
Union
> probability that either A, or B, or both occur
that at least one occurs
A ∪ B
mutually exclusive
> no intersection between A and B
mutually exclusive formula
𝑃 (𝐴 ∪ 𝐵) = 𝑃 (𝐴) + 𝑃 (𝐵)
exhaustive
union represents full sample space
union formula (not mutually exclusive)
𝑃 (𝐴 ∪ 𝐵) = 𝑃(𝐴) + 𝑃(𝐵) − 𝑃(𝐴 ∩ 𝐵)
conditional probability of a given b formula
𝑃(𝐴|𝐵) = 𝑃(𝐴 ∩ 𝐵)/𝑃(𝐵)
conditional rule for independence
if A and B are independent
𝑃(𝐴|𝐵) = 𝑃(𝐴) and 𝑃(𝐵|𝐴) = 𝑃(𝐵)
Bayes theorem
𝑃(B|A) = 𝑃(A|B)P(B) / P(A)
Difference between probability mass function and probability density function?
> pmf relates to a discrete sample space
pdf relates to a continuous sample space
E[X] (𝜇)
sum of the x * p(x)
(if discrete)
var[X]
E[X^2] - (E[X])^2
E[X+b]
E[X] + b
E[aX]
aE[X]
var[aX+b]
a^2var[X]
integration
> increase power of terms by 1 and divide by new power.
How to show that f(x) is a valid pdf?
need to show that the integral over the full sample space is equal to 1
cor[X,Y]
cov[X,Y]/s.d(A)*s.d(B)
