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We see a pattern but not one as simple as the binomial expansion we saw previously So we see that like adjacent results are almost certain to occur somewhere in the sequence that is the sample point The mean number of runs is 3 If a group is asked to write down a sequence of, say, G s and D s, they are likely to write down too many runs; like symbols are very likely to occur together In a baseball season of 162 games, it is virtually certain that runs of several wins or losses will occur These might be noted as remarkable in the press; they are not We will explore the topic of runs more thoroughly in 12 One usually has a number of choices for the sample space In this example, we could choose the sample space that has 32 points or the sample space {0, 1, 2, 3, 4, 5} indicating the number of good items or the set {1, 2, 3, 4, 5} showing the number of runs So we have three possible useful sample spaces Is there a correct sample space The answer is no The sample space chosen for an experiment depends upon the probabilities one wishes to calculate Very often one sample space will be much easier to deal with than another for a problem, so alternative sample spaces provide different ways for viewing the same problem As we will see, the probabilities assigned to these sample points are quite different We should also note that good and defective items usually do not come off production lines at random Items of the same sort are likely to occur together The frequency of defective items is usually extremely small, so the sample points are by no means equally likely We will return to this when we consider acceptance sampling in 2 and statistical process control in 11.

EIN OMB No 1545-0003

.

When you create a new semaphore object, you must always specify an initial and maximum count In the C re a t eSema p h o r e APIs, this is accom plished with l I n i t i a l C o u n t and IMa x i mumCo u nt, respectively, while Sem a p h o re's constructors offer i n i t i a l C o u n t and m a x imumCo u n t parameters As noted in the introduction to this section, a semaphore is signaled so long as its current count is non-O The initial count given is the semaphore object's current count once it has been created, and the maximum count will ensure any attempts to increment the semaphore's count above the maximum number will fail (The maximum is inclusive: that is, it is legal for a semaphore to take on the value of its maximum) For obvious reasons, the initial count may not be greater than the maximum As with mutex objects, if you try to create a new semaphore with the same name as an existing semaphore kernel object on the machine, the resulting reference will refer to the existing semaphore rather than a new one In such a case, G et L a s t E r r o r will return E R RO R_A L R E ADY_EXISTS for C r e a t eSema p h o r e or C re a t eSema p h o r e E x, and the c re a t ed New output parameter for the managed S e m a p o h o re's constructor will be set to false This situation is not nearly as important to check for as with mutexes because the calling thread doesn' t "own" the semaphore, but it does mean the specified counts will have been ignored This may or may not be a prob lem for your code; it depends on the situation.

Windows XP thread pool has, by far, the worst performance of the bunch Though the difference between Vista and XP appears small in this graph, in reality, the XP thread pool only provides 1 2 percent of the callback throughput of Vista We will conclude by looking at some scaling numbers We compare the execution time of running N tasks each comprising of C cycles on a single thread versus queuing each of the N tasks to run on the P thread pool threads, where P is the number of processors on the machine Each of the threads will receive N /P tasks and, for each one, run C cycles' worth of sim ulated work In all measurements, we show the CLR 20 SPI and Windows Vista thread pools side-by-side, and, in all cases, prime the pools to ensure we don't measure the cost of lazily allocating the threads In summary, the single threaded case will execute in roughly O(NC) time, while the thread pool case will execute in O(Q + (CNS) / P), where Q is the overhead that results from using the pool (we measure the calls to

The numbers 1, 2, 3, and 4 are arranged in a line at random The sample space here consists of all the possible orders, as shown below

(Rev December 2001)