The expectation of the ratio of independent random variables, specifically for identically distributed variables x_1, x_2, ..., x_n taking values in the interval (1, 2), is derived from the expression y = x_1/(x_1 + ... + x_n). The hint provided indicates that E[(x_1 + ... + x_n)/(x_1 + ... + x_n)] equals 1, which simplifies the calculation of the expectation of y. The conclusion is that the expected value of y can be computed using properties of linearity of expectation and the characteristics of the uniform distribution over the specified interval.
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