01. Probability.pdf - IMSE2132 Bill KP Chan Office HW8-14...

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IMSE2132 Bill KP Chan Office: HW8-14 Tel.: 2859 7059 Email: [email protected]
Statistical experiment : uncertainty in outcome E.g., throw two coins . Sample space : set of all possible outcomes ࠵? = ࠵?࠵? , ࠵?࠵? , ࠵?࠵? , ࠵?࠵? Event : a subset of sample space ࠵? = ࠵?࠵? ࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵? ࠵?࠵?࠵?࠵? ࠵? = ࠵?࠵? ࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵? ℎ࠵?࠵?࠵? Intersection ࠵? ∩ ࠵? the set of all outcomes in A AND B. Union : ࠵? ∪ ࠵? the set of all outcomes in A OR B. Compliment : ࠵? 5 = ࠵? − ࠵? the set of all outcomes NOT in A ࠵? − ࠵? = ࠵? ∩ ࠵? 5 the set of all outcomes in A but not in B. Universal event : ࠵? Null event :
Statistical experiment, Sample space: ࠵? , Event: ࠵?, ࠵? Intersection: ࠵? ∩ ࠵? Union: ࠵? ∪ ࠵? Compliment: ࠵? 5 = ࠵? − ࠵? ࠵? − ࠵? = ࠵? ∩ ࠵? 5 Universal event: ࠵? , Null event: Mutually exclusive: ࠵? ∩ ࠵? = ∅ Venn Diagram A B S A B S A B S A B S A B S ࠵? ∩ ࠵? ࠵? ∪ ࠵? ࠵? − ࠵? or ࠵? ∩ ࠵? 5 A B S
Statistical experiment, Sample space: ࠵? , Event: ࠵?, ࠵? Intersection: ࠵? ∩ ࠵? Union: ࠵? ∪ ࠵? Compliment: ࠵? 5 = ࠵? − ࠵? ࠵? − ࠵? = ࠵? ∩ ࠵? 5 Universal event: ࠵? , Null event: Mutually exclusive: ࠵? ∩ ࠵? = ∅ Venn Diagram A B S A B S A B S A B S A B S ࠵? ∩ ࠵? ࠵? ∪ ࠵? ࠵? − ࠵? or ࠵? ∩ ࠵? 5 A B S ࠵? 5
Statistical experiment, Sample space: ࠵? , Event: ࠵?, ࠵? Intersection: ࠵? ∩ ࠵? Union: ࠵? ∪ ࠵? Compliment: ࠵? 5 = ࠵? − ࠵? ࠵? − ࠵? = ࠵? ∩ ࠵? 5 Universal event: ࠵? , Null event: Mutually exclusive: ࠵? ∩ ࠵? = ∅ Venn Diagram A B S A B S A B S A B S A B S ࠵? ∩ ࠵? ࠵? ∪ ࠵? ࠵? − ࠵? or ࠵? ∩ ࠵? 5 A B S ࠵? 5 or ࠵? ∪ ࠵? − (࠵? ∩ ࠵?) ࠵? − ࠵? ∪ (࠵? − ࠵?)
Statistical experiment, Sample space: ࠵? , Event: ࠵?, ࠵? Intersection: ࠵? ∩ ࠵? Union: ࠵? ∪ ࠵? Compliment: ࠵? 5 = ࠵? − ࠵? ࠵? − ࠵? = ࠵? ∩ ࠵? 5 Universal event: ࠵? , Null event: Mutually exclusive: ࠵? ∩ ࠵? = ∅ Venn Diagram A B S A B S A B S A B S A B S ࠵? ∩ ࠵? ࠵? ∪ ࠵? ࠵? − ࠵? or ࠵? ∩ ࠵? 5 A B S ࠵? 5 or ࠵? ∪ ࠵? − (࠵? ∩ ࠵?) ࠵? − ࠵? ∪ (࠵? − ࠵?) or ࠵? 5 ∪ ࠵? ࠵? − ࠵? 5
Example § If ࠵? = {1,2,3,4,5,6,7,8,9,10} ࠵? = {2,4,6,8,10} is the set of even integers in ࠵? , ࠵? = {1,3,5} , and ࠵? = 2,4,5 § ࠵? 5 = ? § ࠵? ∩ ࠵? = ? § ࠵? ∪ ࠵? ∩ ࠵? = ? § ࠵? and ࠵? mutually exclusive? ? § ࠵? and ࠵? mutually exclusive? ? § ࠵? ∩ ࠵? 5 = ? § ࠵? − ࠵? 5 = ? § ࠵? − ࠵? ∩ ࠵? = ?
Example § If ࠵? = {1,2,3,4,5,6,7,8,9,10} ࠵? = {2,4,6,8,10} is the set of even integers in ࠵? , ࠵? = {1,3,5} , and ࠵? = 2,4,5 § ࠵? 5 = ? § ࠵? ∩ ࠵? = § ࠵? ∪ ࠵? ∩ ࠵? = ? § ࠵? and ࠵? mutually exclusive? ? § ࠵? and ࠵? mutually exclusive? ? § ࠵? ∩ ࠵? 5 = ? § ࠵? − ࠵? 5 = ? § ࠵? − ࠵? ∩ ࠵? = ? 1,3,5,7,9
Example § If ࠵? = {1,2,3,4,5,6,7,8,9,10} ࠵? = {2,4,6,8,10} is the set of even integers in ࠵? , ࠵? = {1,3,5} , and ࠵? = 2,4,5 § ࠵? 5 = ? § ࠵? ∩ ࠵? = ? § ࠵? ∪ ࠵? ∩ ࠵? = ? § ࠵? and ࠵? mutually exclusive? ? § ࠵? and ࠵? mutually exclusive? ? § ࠵? ∩ ࠵? 5 = ? § ࠵? − ࠵? 5 = ? § ࠵? − ࠵? ∩ ࠵? = ? 1,3,5,7,9 2,4
Example § If ࠵? = {1,2,3,4,5,6,7,8,9,10} ࠵? = {2,4,6,8,10} is the set of even integers in ࠵? , ࠵? = {1,3,5} , and ࠵? = 2,4,5 § ࠵? 5 = ? § ࠵? ∩ ࠵? = ? § ࠵? ∪ ࠵? ∩ ࠵? = ? § ࠵? and ࠵? mutually exclusive? ? § ࠵? and ࠵? mutually exclusive? ? § ࠵? ∩ ࠵? 5 = ? § ࠵? − ࠵? 5 = ? § ࠵? − ࠵? ∩ ࠵? = ? 1,3,5,7,9 2,4 1,2,3,4,5
Example § If ࠵? = {1,2,3,4,5,6,7,8,9,10} ࠵? = {2,4,6,8,10} is the set of even integers in ࠵? , ࠵? = {1,3,5} , and ࠵? = 2,4,5 § ࠵? 5 = ? § ࠵? ∩ ࠵? = ? § ࠵? ∪ ࠵? ∩ ࠵? = ? § ࠵? and ࠵? mutually exclusive? § ࠵? and ࠵? mutually exclusive? ? § ࠵? ∩ ࠵? 5 = ? § ࠵? − ࠵? 5 = ? § ࠵? − ࠵? ∩ ࠵? = ? ࠵?࠵?࠵? 1,3,5,7,9 2,4 1,2,3,4,5
Example § If ࠵? = {1,2,3,4,5,6,7,8,9,10} ࠵? = {2,4,6,8,10} is the set of even integers in ࠵? , ࠵? = {1,3,5} , and ࠵? = 2,4,5 § ࠵? 5 = ? § ࠵? ∩ ࠵? = ? § ࠵? ∪ ࠵? ∩ ࠵? = ? § ࠵? and ࠵? mutually exclusive?