# Basic Expected Value Problem (probability)

• shawn87411
In summary, the expected value of the given function is 2 and the variance is 3. Using the linearity properties of expected value, we can find E(X^2) to be 7.
shawn87411
E[X]=2
Var(X)=3
Find E[4+4x+x^2]

I'm just confused what its asking. The expected value of this function is 2 so the average of it is 2 and the variance is how much it varies which is 3? Every example I have for expected values is related to an example such as cards, not just a polynomial

Var(X)=E(X^2-E(X)^2). Just solve that for E(X^2). Then you can find E of the quadratic.

Dick said:
Var(X)=E(X^2-E(X)^2). Just solve that for E(X^2). Then you can find E of the quadratic.

Is the E(X^2-E(X)^2) = E(2^2-(4+4x+X^2)^2)?

No... Var(X)=3=E(X^2)-E(X)^2. E(X)=2. What's E(X^2)?? E(4+4X+X^2)=E(4)+E(4X)+E(X^2). Right? Etc. Use the linearity properties of 'E'.

Last edited:
Dick said:
No... Var(X)=3=E(X^2)-E(X)^2. E(X)=2. What's E(X^2)?? E(4+4X+X^2)=E(4)+E(4X)+E(X^2). Right? Etc.

I think I'm mixing up the terms E(X^2) and e(X)^2. Which one is E[X]=2?

So E(X^2)=E(4)^2+E(4x)^2+(x^2)^2?

E(X)^2=4, since E(X)=2.

Dick said:
E(X)^2=4, since E(X)=2.

Right but what's the difference between E(X^2) and E(X)^2?

Is E(X^2)=E(4^2)+E(4x^2)+E((x^2)^2) with x=2?

No! E(X^2) is not the same as E(X)^2. They aren't directly related to each other. The only way you can find E(X^2) from the information you are given is to use Var(X)=3.

Var(X)+E(X)^2=E(X^2)
3+4=7=E(x^2)

Then use the fact that E(4+4X+X^2)=E(4)+E(4X)+E(X^2).

shawn87411 said:
Var(X)+E(X)^2=E(X^2)
3+4=7=E(x^2)

Then use the fact that E(4+4X+X^2)=E(4)+E(4X)+E(X^2).

Yes, that's it.

## 1. What is a basic expected value problem in probability?

A basic expected value problem in probability involves calculating the average outcome of a random event or experiment. It is used to determine the most likely outcome of a situation based on the given probabilities.

## 2. How do you calculate expected value in probability?

To calculate expected value in probability, you multiply each possible outcome by its corresponding probability and then add all of these values together. This gives you the average outcome or expected value.

## 3. What is the significance of expected value in probability?

Expected value is significant because it allows us to make informed decisions by predicting the most likely outcome of a random event. It is also a key concept in statistics and decision-making, as it helps us understand the risks and rewards associated with different choices.

## 4. Can expected value be negative?

Yes, expected value can be negative. This means that on average, the outcome of a random event will result in a loss rather than a gain. It is important to consider both positive and negative expected values when making decisions.

## 5. How is expected value used in real life?

Expected value is used in various real-life situations, such as in insurance, finance, and gambling. For example, insurance companies use expected value to calculate premiums based on the likelihood of an event occurring. In finance, expected value is used to determine the potential return on investment. In gambling, expected value is used to calculate the odds of winning and losing in different games.

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