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Unformatted text preview: AMS 507 Recitation 3 Xiaoping Zhou November 1, 2010 Problem 5.30 An image is partitioned into two regions, one white and the other black. A reading taken from a randomly chosen point in the white section will give a reading that is normally distributed with = 4 and 2 = 4 , whereas one taken from a randomly chosen point in the black region will have a normally distributed reading with parameters (6,9). A point is randomly chose on the image and has a reading of 5. If the fraction of the image that is black is , for what value would be the probability of making an error be the same, regardless of whether one concluded that the point was in the black region or in the white region? Analysis There are a lot inquiries about this problem. First of all, we need to know what kind of distribution of the readings on the image it is. Intuitively, the reading cannot be a continuous & unbounded distribution, other wise, the probability that you picking up a point reading of 5 is always zero. Let us understand the problem in this way: the true values on the image are continuous, while the obsevered reading values are discrete value s. When we get a reading of 5, the actual value resides in a short interval around 5, say...
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This note was uploaded on 01/31/2011 for the course AMS 507 taught by Professor Feinberg,e during the Spring '08 term at SUNY Stony Brook.
- Spring '08