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

schnappifx

New member
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 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!
 

Attachments

Last edited by a moderator:

tkhunny

Moderator
Staff member
Joined
Apr 12, 2005
Messages
9,819
It seems prudent to start with eth Mean and Variance of the Distribution. How did you arrive at 1 and 1?
 
Top