schnappifx
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 Joined
 Sep 8, 2017
 Messages
 2
Hi all,
I am struggling with a problem from machine learning 101, here is the problem (problem 3)
Problem 3
Let x_{i}: i = 1, ..., N, be a sample of N independent, identically distributed random variables drawn from the uniform distribution over [0, 2]; that is:
. . . . .\(\displaystyle p(x)\, =\, \begin{cases}0&\mbox{if }\, x\, <\, 0\, \mbox{ or }\, x\, >\, 2\\0.5&\mbox{if }\, 0\, \leq\, x\, \leq\, 2\end{cases}\)
Now consider
. . . . .\(\displaystyle \displaystyle m_N\, =\, \dfrac{1}{N}\, \sum_{i=1}^N\, x_i\)
that is, the sample mean (average) of the xs. The variable m_{N} is a random variable itself. What are its mean and its variance?
(End of Problem 3)
I thought the mean of m_{N} should be 1 and so is the variance...but is that too simple?
Thanks!
I am struggling with a problem from machine learning 101, here is the problem (problem 3)
Problem 3
Let x_{i}: i = 1, ..., N, be a sample of N independent, identically distributed random variables drawn from the uniform distribution over [0, 2]; that is:
. . . . .\(\displaystyle p(x)\, =\, \begin{cases}0&\mbox{if }\, x\, <\, 0\, \mbox{ or }\, x\, >\, 2\\0.5&\mbox{if }\, 0\, \leq\, x\, \leq\, 2\end{cases}\)
Now consider
. . . . .\(\displaystyle \displaystyle m_N\, =\, \dfrac{1}{N}\, \sum_{i=1}^N\, x_i\)
that is, the sample mean (average) of the xs. The variable m_{N} is a random variable itself. What are its mean and its variance?
(End of Problem 3)
I thought the mean of m_{N} should be 1 and so is the variance...but is that too simple?
Thanks!
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