# Machine Learning 101: Let x_i be N i.i.d random vars drawn from uniform dist. over...

#### schnappifx

##### New member
Hi all,

I am struggling with a problem from machine learning 101, here is the problem (problem 3)

Problem 3
Let xi: 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 mN is a random variable itself. What are its mean and its variance?

(End of Problem 3)

I thought the mean of mN should be 1 and so is the variance...but is that too simple?
Thanks!

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#### tkhunny

##### Moderator
Staff member
It seems prudent to start with eth Mean and Variance of the Distribution. How did you arrive at 1 and 1?