Summary Probability and Statistics for International Business Administration, lecture notes
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Course
Probability and Statistics
Institution
Universiteit Twente (UT)
Lecture notes of all the Probability lectures given by K. Poortema in BOM (module 2 of IBA at the UT). Includes all the useful formulas and explanations.
Probability for International Business Administration, Lecture 1
Probability and Statistics
11-12-2018, K. Poortema
Probability theory treats only known data (different from statistics, where we also treat
unknown data/models)
When rolling 2 dices, probability of a number on one dice is 1/6. For a number on one dice,
and a number on the other dice is 1/6 * 1/6 = 1/36 (probability for each number is equal for
each dice). A set A ={(1,3), (2,2), (4,3)} has a probability of 3/36 to occur.
A is the set, Ac is the complementary of A à So, all the values that are not within, but
outside A. You can calculate the probability for Ac: P(Ac) = 1 – P(A).
Probability you pick A or B
P(A or B) = P(A) + P(B) – P(A and B)
Sample space S = {all outcomes}
Event A: a subset of S
“certain event” is the largest A you can find, this is S (P(A) = 1)
“impossible event” is the smallest A you can find, noted as Æ, P(Æ) = 0
Intersection, Ç , both P(A) and P(B) occur
Union, È , both P(A), P(B) and, P(A and B)
Two subsets are mutually exclusive (disjoint) if their intersection is empty, P(A and C) = 0
Product rule (conditional probability)
Conditional probability of A given B
𝑃(𝐴 ∩ 𝐵)
𝑃(𝐴|𝐵) =
𝑃(𝐵)
𝑃(𝐴 ∩ 𝐵) = 𝑃(𝐴|𝐵) ∗ 𝑃(𝐵)
𝑃(𝐴 ∩ 𝐵) = 𝑃(𝐵|𝐴) ∗ 𝑃(𝐴)
Conditional probability of B given A
𝑃(𝐵 ∩ 𝐴)
𝑃(𝐵|𝐴) =
𝑃(𝐴)
𝑃(𝐴 ∩ 𝐵) = 𝑃(𝐵|𝐴) ∗ 𝑃(𝐵)
Note the difference of P(B) and P(A|B)
, Product rule for independent events A and B:
𝑃(𝐴 ∩ 𝐵) = 𝑃(𝐴) ∗ 𝑃(𝐵)
If A and B are independent, then:
𝑃(𝐴|𝐵) = 𝑃(𝐴)
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