Simple question about expected value

In summary, expected value is a statistical concept used to determine the average outcome of a random variable over a large number of trials. It is calculated by multiplying each possible outcome by its probability and adding all of these values together. Expected value is important because it allows for informed decision-making based on probabilities and helps to understand potential outcomes and risks. It is calculated by multiplying each possible outcome by its probability and adding all of these values together, and can be represented by the formula E(x) = Σx * P(x). The expected value may not always match the actual outcome, but over a large number of trials, it will converge to the actual outcome. Additionally, expected value can be negative if the possible outcomes include negative values, but it
  • #1
pamparana
128
0
Hello,

Just came across this that:

E[cos(t)sin(t)] = 0

the expected value of the product of cos(t)sin(t) is 0. However, I am unable to convince myself that is the case. Can anyone help me understand why this is so?

Many thanks,

Luc
 
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  • #2
I suppose the probability space is [itex][0,2 \pi)[/itex] with normalized Lebesgue measure? In that case, what it means is
[tex]
\frac{1}{2\pi}\int_0^{2\pi} \sin(t) \cos(t)\,dt = 0
[/tex]
 

What is expected value?

Expected value is a statistical concept that represents the average outcome of a random variable over a large number of trials. It is calculated by multiplying each possible outcome by its probability and adding all of these values together.

Why is expected value important?

Expected value allows us to make informed decisions based on probabilities. It helps us understand the potential outcomes and risks associated with a particular situation or event.

How is expected value calculated?

Expected value is calculated by multiplying each possible outcome by its probability and adding all of these values together. This formula can be written as E(x) = Σx * P(x), where x represents the possible outcomes and P(x) represents the probability of each outcome.

What is the relationship between expected value and actual outcomes?

Expected value is an average of all possible outcomes, so it may not always match the actual outcome. However, over a large number of trials, the expected value will converge to the actual outcome.

Can expected value be negative?

Yes, expected value can be negative if the possible outcomes include negative values. It is simply a mathematical calculation and does not necessarily reflect the actual outcome.

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