(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose x = (x1, x2, ..., xn)T ∈ Rn is a random vector drawn from the n-dimensional

standard Gaussian distribution N(0, I), where 0 = (0, 0, ..., 0)^T (0 vector transpose) and I is the identity matrix.

(a) What distribution does ||x||^2 follow? Justify your answer.

(b) On the average, how far away (in terms of squared Euclidean distance) from the

origin do you expect x to be? In other words, what is E(||x||^2)?

(c) Now suppose we fix x and draw another random vector z from N(0, I). If we

project z onto the direction of x, how far away from the origin (again, in terms of squared

Euclidean distance) do you expect the projection to be? (Hint: Let u be the unit vector

pointing in the direction of x. Then, uT z is the projection of z onto the direction of x.

Find the expectation and variance of uT z conditional on u.)

2. Relevant equations

3. The attempt at a solution

no attempt... don't even understand the question... :P

Thanks guys... ur help is greatly appreciated...

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# Homework Help: Applied Stats Help - Don't even understand the question

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