### Value of mean that maximizes the function of mean

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Let Y be the jumping distance of a flea. It is known that Y is normally distributed and that its standard deviation is one inch. One flea is observed jumping and the distance it jumps is recorded (Think of this as taking a sample of size one). Consider f(y), the density of a normal distribution with std = 1. In this case y is a fixed, known value. It is mew that is unknown. As such think of f(y) as a function of mew: That is, think of it as f(mew): Find the value of mew that maximizes f(mew): We can think of this as the value of mew that maximizes f(y), the probability that our observed value of y occurs.

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