slide 16 disjoint - quantitative sciences course...
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Slide 16
1. Disjoint
2. Not disjoint
3. Disjoint
4. Not disjoint
5. Disjoint
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Since P(E)+P(Ē) = 1
P(E) = 1-P(Ē)
Slide 26 This is a different question, but it is really similar.
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The set of all possible realizations is called the SUPPORT or RANGE of X
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a. P(2≤x≤4) = P(1<x≤4) = F(4)-F(1) = 16/36 – 1/36 = 15/36
b. P(4≤x≤6) = P(3<x≤6) = F(6)-F(3) = 36/36 – 9/36 = 27/36
c. P(2<x≤5) = F(5)-F(2) = 25/36 – 4/36 = 21/36
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E[X] = 1(1/36) + 2(3/36) + 3(5/36) + 4(7/36) + 5(9/36) + 6(11/36)
= 161/36
Slide 71 (5.1 and 5.2 is proof, it’s up to you if you want to go over those)
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