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compressive strength 5500 psi and the standard deviation is 100 psi. Find the probability that the sample mean compressive strength exceeds 4985 psi. 7-54. A normal population has a known mean 50 and known variance 2 2. A random sample of n 16 is selected from this population, and the sample mean is x 52. How unusual is this result 7-55. A random sample of size n 16 is taken from a normal population with 40 and 2 5. Find the probability that the sample mean is less than or equal to 37. 7-56. A manufacturer of semiconductor devices takes a random sample of 100 chips and tests them, classifying each chip as defective or nondefective. Let Xi 0 if the chip is nondefective and Xi 1 if the chip is defective. The sample fraction defective is

p 100

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Every display object owns a coordinate space, a frame of reference against which the contents of the display object are measured. Positions, rotations, and distances in ActionScript are expressed in pure numbers. Of course, these naked numbers are meaningless without units like pixels (distance) or degrees (rotation), but they are also meaningless without a coordinate space to exist in. The coordinate space tells you what the x and y axes are, where those axes meet to form the origin (0, 0), and how far one unit is. Even though it s easy to forget about it, all measurements are relative to some frame of reference or other. When you measure the height of a building, it s understood that you re speaking about the height directly up starting at the ground you could just as easily measure the height of the building from sea level instead and get a much different result. When I tell you to go north in Manhattan, I m actually asking you to travel along the avenues north-south axis, which is nowhere

The annotations are not intended to be an exhaustive list, and we expect that they will be modified to suit the particular application domain and the services available in the target deployment For instance, the current set of task annotations allows placement based on node IDSor locations This can be generalized to placement based on context hbels The idea of context labels is employed in EnviroTrack [ 13 as a mechanism to address sensor nodes and also to host context-specific computation The idea behind context labels is to allow the user to specify dynamic behaviors based on the current state of a node The fraction of total energy reserves currently remaining in the node can be considered as a context This context can be used as a task annotation to specify alternate implementations of the same task and tag each implementation with the context of its invocation.

X100

near true north 29 degrees to the east, in fact and yet perfectly describes the street grid, making it a much more useful frame of reference. Or simply think of it like this: the salt shaker to my right is on your left when you sit across from me. Measurements are always relative to a frame of reference.

What is the sampling distribution of the random variable P 7-57. Let X be a random variable with mean and variance 2 . Given two independent random samples of sizes n1 and n2, with sample means X1 and X2 , show that X aX1 11 a2 X2, 0 a 1

FIGURE 14-1

is an unbiased estimator for . If X1 and X2 are independent, nd the value of a that minimizes the standard error of X . 7-58. A random variable x has probability density function f 1x2 1 2 xe 2 3

The coordinate system of each display object is its local coordinate system. If you ve created a movie clip in Flash Professional and edited its contents by opening the symbol in the library, you ve worked in the symbol s local coordinate system. Suddenly, whatever rotations, translations, scaling, and shearing (collectively known as transformations) you ve applied to any given instance of the symbol doesn t matter, and you re presented with the clip in its own context. It has an origin the registration point from which the x and y axes emanate to the right and down. In the local coordinate space, one unit is one pixel, and y coordinates increase as they go down, unlike the canonical Cartesian coordinate space with y increasing up. In short, the local coordinate system is the natural space of a display object.

Find the maximum likelihood estimator for . 7-59. Let f 1x2 x 1, 0 , and 0 x 1. n Show that n 1ln w i 1 Xi 2 is the maximum likelihood estimator for . 7-60. Let f 1x2 11 2x 11 2 , 0 x 1, and 0 . n Show that 11 n2 g i 1 ln1Xi 2 is the maximum likelihood estimator for and that is an unbiased estimator for .

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