a?? n Example 2.10, identify three events that are mutually exclusive. b?. ?Suppose there is no outcome common to all three of the events ?A, B, ?and ?C. ?Are these three events necessarily mutually exclusive? If your answer is yes, explain why; if your answer is no, give a counterexample using the experiment of Example 2.10. Reference example 2.10 A small city has three automobile dealerships: a GM dealer selling Chevrolets and Buicks; a Ford dealer selling Fords and Lincolns; and a Toyota dealer. If an experiment consists of observing the brand of the next car sold, then the events ?A ={Chevrolet, Buick}and ?B={?Ford, Lincoln} are mutually exclusive because the next car sold cannot be both a GM product and a Ford product (at least until the two companies merge!). The operations of union and intersection can be extended to more than two events. For any three events ?A, B, ?and ?C, ?the event A ???B ?& ??C is the set of outcomes contained in at least one of the three events, whereas ?A ?´ ??B ´ ??C is the set of outcomes contained in all three events. Given events A1,A2,A3,…….., these events are said to be mutually exclusive (or pairwise disjoint) if no two events have any outcomes in common. A pictorial representation of events and manipulations with events is obtained by using Venn diagrams. To construct a Venn diagram, draw a rectangle whose interior will represent the sample space . Figure 2.1 shows examples of Venn diagrams.

Answer : Step 1 : Consider the strength data for beams given the data in below. 5.9 8.2 7.2 8.7 7.3 7.8 6.3 9.7 8.1 7.4 6.8 7.7 7 9.7 7.6 7.8 6.8 7.7 6.5 11.6 7 11.3 6.3 11.8 7.9 10.7 9 a). Now we have to construct a stem-and-leaf display of the data. What appears to be a representative strength value. Stem Leaf 5 9 6 3 3 5 8 8 7 0 0 2 3 4 6 7 7 8 8 9 8 1 2 7 9 0 7 7 10 7 11 3 6 8 The stem and leaf is shown above. What constitutes large or small variation usually depends on the application at hand, but an often-used rule of thumb is: the variation tends to be large whenever the spread of the data (the difference between the largest and smallest observations) is large compared to a representative value. Here, 'large' means that the percentage is closer to 100% than it is to 0%. For this data, the spread is 11 - 5 = 6, which constitutes 6/8 = .75, or, 75%, of the typical data value of 8. Most researchers would call this a large amount of variation. Step 2 : b). The data display is not perfectly symmetric around some middle/representative value. The graph is not symmetric. It tails or is skewed toward the greater values.