Mental Blank / Hopefully easy question

  • Thread starter patata
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In summary, the conversation discusses the formula Var[x] + Var[y] - 2Cov(X,Y) and how it is always greater than or equal to 0. The participants mention that this can be derived from (x-y)^2 >=0 and can be simplified using the definitions of variance and covariance. The conversation also touches on the use of means in the formula.
  • #1
patata
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Hi all,

Probably a stupid question, but in general, is it true that Var[x] + Var[Y] -2Cov(X,Y) > 0? I'm having trouble figuring out why a number of articles I seem to have read take this for granted without demonstrating why (which makes me think it could be fairly trivial...).

Thanks for any help!
 
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  • #2
You can derive it from (x-y)^2 >=0
It can be equal to zero, but not negative. Just plug in the definitions of variance and covariance and simplify until you get something like (x-y)^2.
 
  • #3
If you start with {(X - mx) - (Y-my)}2, it follows immediately. (The m's are means).
 

1. What is a mental blank?

A mental blank is a temporary inability to remember or think of something that is usually easily recalled or understood. It is also known as a mental block or a brain freeze.

2. What causes a mental blank?

A mental blank can be caused by various factors such as stress, fatigue, anxiety, lack of sleep, distractions, or even pressure to perform well in a certain situation. It can also be a result of a medical condition or medication side effects.

3. How can I overcome a mental blank?

There are several strategies that can help overcome a mental blank, such as taking a short break and practicing relaxation techniques, focusing on one task at a time, getting enough rest and sleep, staying hydrated and nourished, and using memory aids or techniques like visualization or association. It is also important to address any underlying issues causing the mental blank.

4. Is a mental blank a sign of a serious problem?

In most cases, a mental blank is a normal and temporary occurrence and is not a sign of a serious problem. However, if it happens frequently and affects daily functioning, it may be a symptom of an underlying medical or mental health condition and it is best to consult a healthcare professional.

5. Can mental blanks be prevented?

While it may not be possible to completely prevent mental blanks, certain lifestyle changes and habits can help reduce their frequency. These include managing stress levels, getting enough rest and sleep, staying physically active, and practicing memory exercises or techniques. It is also important to address any underlying issues that may be contributing to the mental blanks.

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