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Suppose that an object is 10 inches long and suppose that a measuring device gives the readings 7 inches with probability 1/4, 9 inches with probability 1/4, 11 inches with probability 1/4 and 13 inches with probability 1/4. Write down all 16 possible ways that two measurements can turn out. Put a check mark by those possibilities where one measurement is above 10 and the other measurement is below 10, i.e. where high measurements tend to cancel low measurements. Use these possibilities to compute the distribution of when n = 2(i.e., find , , etc.).
A variation of the binomial distribution arises when the n trials are all independent, but the probability of a success on the ith trial is θi, and these probabilities are
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