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jimbodonut
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Homework Statement
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.)
Homework Equations
The Attempt at a Solution
no attempt... don't even understand the question... :P
Thanks guys... ur help is greatly appreciated...