Question
In: Math
1. Can two variables share a deterministic relationship, and yet be uncorrelated? For instance, suppose that...
1. Can two variables share a deterministic relationship, and
yet be uncorrelated? For instance, suppose that X follows a
continuous, uniform distribution between −1 and 1:
X ~ U[−1, 1].
a. Draw a graph of the distribution of X.
By a symmetry argument—the distribution of X is symmetric
around zero—it is clear that E(X) = 0.
Now let Y = X2.
b. Clearly Y and X are not independent; in fact, a
deterministic relationship exists between them (if you know X, you
know Y). Show, however, that X and Y are uncorrelated: Cov(X,Y) =
0. Hint: use a symmetry argument for the distribution of X3.
c. Can you explain why there is no correlation despite an
obvious relationship?
Solutions
milcah answered 1 year agoRelated Solutions
1. Can two variables share a deterministic relationship, and yet be uncorrelated? For instance, suppose that...
1. Can
two variables share a deterministic relationship, and yet be
uncorrelated? For instance, suppose that X follows a continuous,
uniform distribution between −1 and 1:
X ~
U[−1, 1].
a.
Draw a graph of the distribution of X.
By a
symmetry argument—the distribution of X is symmetric around zero—it
is clear that E(X) = 0.
Now
let Y = X2.
b.
Clearly Y and X are not independent; in fact, a deterministic
relationship exists between them (if you know...
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public class OperationsBetween { // You must define the following: // 1.) Two private instance variables,...
public class OperationsBetween {
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