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...
public class OperationsBetween { // You must define the following: // 1.) Two private instance variables,...
public class OperationsBetween {
// You must define the following:
// 1.) Two private instance variables, min and
max
// 2.) A constructor which takes initial values for
// min and max
// 3.) An instance method named sum, which sums the
// values between min and max and returns the
// result. For example, if min = 3 and max = 5,
// then this should return 12 (3 + 4 + 5). If
// min is greater than...
public class OperationsBetween { // You must define the following: // 1.) Two private instance variables,...
public class OperationsBetween {
// You must define the following:
// 1.) Two private instance variables, min and max
//
// 2.) A constructor which takes initial values for
// min and max
//
// 3.) An instance method named sum, which sums the
// values between min and max and returns the
// result. For example, if min = 3 and max = 5,
// then this should return 12 (3 + 4 + 5). If
// min is...
(a) What is a class? What is an object? What is the relationship? (b) What are the instance variables and methods of a class?
(a) What is a class? What is an object? What is the relationship? (b) What are the instance variables and methods of a class? (c) What is the effect of declaring instance variables and methods public or private? (d) Why do we often declare the instance variables of classes private? (e) Could we declare methods private? Would we want to do so? (f) What does the identifier this mean? Give an example of its use (g) What is a constructor? (h) What is inheritance? Why is...
1. Direct relationship: A relationship between two variables, where a change in one variable results in...
1. Direct relationship: A relationship between two variables,
where a change in one variable results in the same change in the
other variable. For example, if one variable is increased, then the
other variable will also increase.
Indirect relationship: A relationship between two variables,
where a change in one variable results in the opposite change in
the other variable. For example, if one variable is increased, then
the other variable will decrease.
a. Considering the terms described above, do the...
Suppose that X1 and X2 are two random variables. Suppose that X1 has mean 1 and...
Suppose that X1 and X2 are two random variables. Suppose that X1
has mean 1 and variance 4 while X2 has mean 3 and variance 9.
Finally, suppose that the correlation between X1 and X2 is 3/8.
Denote Y = 2X1 − X2. (67) The mean of Y is (a) 1 (b) 4 (c) -2 (d)
-1 (68) The variance of Y is (a) 25 (b) 4 (c) 9 (d) 16 (69) The
standard deviation of Y is (a) 5...
Code in Java Write a Student class which has two instance variables, ID and name. This...
Code in Java
Write a Student class which has two instance variables, ID and
name. This class should have a two-parameter constructor that will
set the value of ID and name variables. Write setters and getters
for both instance variables. The setter for ID should check if the
length of ID lies between 6 to 8 and setter for name should check
that the length of name should lie between 0 to 20. If the value
could not be set,...
Design a LandTract class that has two fields (i.e. instance variables): one for the tract’s length(a...
Design a LandTract class that has two fields (i.e. instance
variables): one for the tract’s length(a double), and one for the
width (a double). The class should have:
a constructor that accepts arguments for the two fields
a method that returns the tract’s area(i.e. length *
width)
an equals method that accepts a LandTract object as an
argument. If the argument object
holds the same data (i.e. length and width) as the calling
object, this method should...
Design a LandTract class that has two fields (i.e. instance variables): one for the tract’s length(a...
Design a LandTract class that has two fields (i.e. instance
variables): one for the tract’s length(a double), and one for the
width (a double). The class should have:
a constructor that accepts arguments for the two fields
a method that returns the tract’s area(i.e. length *
width)
an equals method that accepts a LandTract object as an
argument. If the argument object
holds the same data (i.e. length and width) as the calling
object, this method should...
1. Implement the Vehicle class. Add the following private instance variables to the Accoun class:...
1. Implement the Vehicle class.
Add the following private instance variables to the Accoun
class:
• An instance variable called wheelsCount of type int
• An instance variable called vType of type String
• An instance variable called isTruck of type boolean .
Add getters and setters for the three instance variables
Add the following methods to the Account class:
• A void method called initialize that takes a parameter of type
int, a String,and one double...
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- Discuss the significance of a proposal What elements do you think are needed for the proposal...
- 1) Given the following equations: QD = 5,000 + 0.5 I + 0.2 A -...
- How has the Supreme Court's Citizens United decision changed campaigns in America? (long answer is appreciated...
- You are a Derivatives Trader at a major Broker-Dealer. At the end of the week you...
- What are the two reasons that limit the ability of correlational studies to provide information on...
- Suppose that 20 monthly payments of $100 each are followed by 30 monthly payments of $200...
- D. Explain what it means for recommendations to be specific and actionable. E. Discuss how charts...
ADVERTISEMENT