Expected Value and Variance Question

In summary, expected value is a measure of the central tendency of a probability distribution, calculated by multiplying each possible outcome by its probability of occurring and summing up the products. It represents the average outcome of a random variable over a large number of trials. In real-life scenarios, expected value can be used to represent the long-term average outcome of a situation with uncertain outcomes, such as in decision-making processes. Variance, on the other hand, measures the spread or variability of a probability distribution by calculating the sum of squared differences between each outcome and the expected value. It shows how much the actual outcomes deviate from the expected value.
  • #1
whitehorsey
192
0
Does μx mean the same thing as E[X]? Also, does σ2x mean the same thing as Var X?
 
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  • #2
Those would be reasonable notations for E[X], Var(X). I wouldn't say it's sufficiently standard to answer more confidently.
 
  • #3
haruspex said:
Those would be reasonable notations for E[X], Var(X). I wouldn't say it's sufficiently standard to answer more confidently.

Okay Thank You!
 

FAQ: Expected Value and Variance Question

1. What is expected value?

Expected value, also known as mean or average, is a measure of the central tendency of a probability distribution. It represents the average outcome of a random variable over a large number of trials.

2. How is expected value calculated?

To calculate the expected value, multiply each possible outcome by its probability of occurring and sum up all the products. This formula is also known as the weighted average formula.

3. What does expected value represent in real-life scenarios?

Expected value can represent the long-term average outcome of a situation with random or uncertain outcomes. For example, it can be used in decision-making processes such as investment analysis or risk assessment.

4. What is variance?

Variance is a measure of the spread or variability of a probability distribution. It represents how far the values of a random variable are spread out from the expected value.

5. How is variance related to expected value?

Variance is calculated by taking the sum of the squared differences between each outcome and the expected value, multiplied by their respective probabilities. In other words, variance measures how much the actual outcomes deviate from the expected value.

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