Robert_V._Hogg,_Joseph_W._McKean,_Allen_T._Craig
1.2. Sets 5 The complement ofAis represented by the white space in the Venn diagram in Panel (a) of Figure 1.2.1. The empty set ...
6 Probability and Distributions B=(2,4), andC=[3, 4 .5). A∪B=(1,4); A∩B=(2,3); B∩C=[3,4) A∩(B∪C)=(1,3)∩(2, 4 .5) = (2,3) (1.2.3) ...
1.2. Sets 7 Example 1.2.4.SupposeCis the interval of real numbers (0,5). SupposeCn= (1−n−^1 ,2+n−^1 )andDn=(n−^1 , 3 −n−^1 ), fo ...
8 Probability and Distributions means the ordinary (Riemann) integral off(x) over a prescribed one-dimensional setAand the symbo ...
1.2. Sets 9 Example 1.2.8.LetCbe the interval of positive real numbers, i.e.,C=(0,∞). LetAbe a subset ofC. Define the set functi ...
10 Probability and Distributions EXERCISES 1.2.1.Find the unionC 1 ∪C 2 and the intersectionC 1 ∩C 2 of the two setsC 1 and C 2 ...
1.2. Sets 11 (c)Ck={(x, y):0≤x^2 +y^2 ≤ 1 /k},k=1, 2 , 3 ,.... 1.2.8.For every one-dimensional setC, define the functionQ(C)= ∑ ...
12 Probability and Distributions 1.3 The Probability Set Function Givenanexperiment,letCdenote the sample space of all possible ...
1.3. The Probability Set Function 13 A probability set function tells us how the probability is distributed over the set of even ...
14 Probability and Distributions That these identities hold for all setsAandBfollows from set theory. Also, the Venn diagrams of ...
1.3. The Probability Set Function 15 For a finite sample space, we can generate probabilities as follows. LetC = {x 1 ,x 2 ,..., ...
16 Probability and Distributions 1.3.1 CountingRules.......................... We discuss three counting rules that are usually ...
1.3. The Probability Set Function 17 bday = function(n){ bday = 1; nm1 =n-1 for(j in 1:nm1){bday = bday*((365-j)/365)} bday < ...
18 Probability and Distributions because there are no difficulties in the determination of the number of elements in each event. ...
1.3. The Probability Set Function 19 Theorem 1.3.6.Let{Cn}be a nondecreasing sequence of events. Then lim n→∞ P(Cn)=P( lim n→∞ C ...
20 Probability and Distributions Theorem 1.3.5 gave a general additive law of probability for the union of two events. As the ne ...
1.3. The Probability Set Function 21 1.3.2.A random experiment consists of drawing a card from an ordinary deck of 52 playing ca ...
22 Probability and Distributions 1.3.11.A person has purchased 10 of 1000 tickets sold in a certain raffle. To determine the fiv ...
1.4. Conditional Probability and Independence 23 1.3.22.Consider the eventsC 1 ,C 2 ,C 3. (a)SupposeC 1 ,C 2 ,C 3 are mutually e ...
24 Probability and Distributions Moreover, from a relative frequency point of view, it would seem logically incon- sistent if we ...
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