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As expected, this probability matches the result obtained from the binomial probability distribu1 4 20.930.11 0.292. The marginal probability distribution for X tion for X; that is, P1X 32 3 is found by summing the probabilities in each column, whereas the marginal probability distribution for Y is found by summing the probabilities in each row. The results are shown in Fig. 5-2. Although the marginal probability distribution of X in the previous example can be determined directly from the description of the experiment, in some problems the marginal probability distribution is determined from the joint probability distribution.

Local Connections and Their Uses .............................................................................................911 Implementing a Local Connection ..............................................................................................912 The Sending Application ..................................................................................................912 Sending Methods to a Receiving Application ........................................................912 Listening for the Status of Local Method Invocations ..........................................913 The Receiving Application ................................................................................................914 Assigning a Delegate .............................................................................................. 914 Listening to a Named Channel ..............................................................................915 Closing the Connection ......................................................................................... 915 Local Connections and the Security Policy ................................................................................915 Specifying the Domain in the Sender .............................................................................. 916 Removing the Domain from the Channel Name .............................................................916 Allowing Cross-Domain Local Connections from the Receiving Application ................ 916 Example: Following the Mouse ...................................................................................................917 Summary ......................................................................................................................................919

y f Y (y) = 0.00004 4 0.00188 3 0.03250 2 0.24925 1 0.71637 0

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Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 921

Figure 5-2 Marginal probability distributions of X and Y from Fig. 5-1.

Object Boolean Function Class String RegExp 2 3 4 6 12 Array Vector XML XMLList Error 8 9 11 11 24 Number int uint Date Math The Flash Player 10.1 API by Number 10 7 7 7 7 7

0 f X (x) = 0.0001

1 0.0036

DisplayObject Shape 35 Bitmap BitmapData InteractiveObject SimpleButton DisplayObjectContainer Sprite MovieClip Graphics 14 14 35 Shader ShaderJob 38 38 Stage 14 Loader LoaderInfo ShaderInput ShaderParameter 27 27 38 38 14 36 36 AVM1Movie 27

2 0.0486

EventDispatcher Event MouseEvent KeyboardEvent FocusEvent 21 21 21 TouchEvent GestureEvent 23 23 TimerEvent FullScreenEvent ProgressEvent NetStatusEvent 20 20 22 14 27 32 20 27 SecurityErrorEvent 27 UncaughtErrorEvent 24

3 0.2916

34 34 15

4 0.6561

34 34 40

De nition If X and Y are discrete random variables with joint probability mass function fXY (x, y), then the marginal probability mass functions of X and Y are fX 1x2 P1X x2 a fXY 1x, y2

Whenever the TargetAlert is received, the Leader task has to determine if sufficient information exists to make a decision on electing itself the leader node (ie, the node closest to the target at that moment) and transmitting the information to the supervisor node Several factors are to be considered while making this decision The first, and the most obvious factor is whether the reading at the local node is greater than the readings received from neighboring nodes Note that we do not handle scenarios where two nodes have the same (and maximum) readings The second factor is what fraction of the neighboring nodes have actually sent the readings Consider the scenario in Figure 521 When the object is at position 0, it is within the sensing radius of nodes 1, 3, and 4 and is detected by the sampling tasks at those three nodes.

(5-2) where Rx denotes the set of all points in the range of (X, Y) for which X Ry denotes the set of all points in the range of (X, Y) for which Y y x and

28 28 32 32

Given a joint probability mass function for random variables X and Y, E(X ) and V(X ) can be obtained directly from the joint probability distribution of X and Y or by rst calculating the marginal probability distribution of X and then determining E(X ) and V(X ) by the usual method. This is shown in the following equation.

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