Variables and normal distributions

In summary, Variables are quantities or characteristics that can take on different values and can be either numerical or categorical. They are related to normal distributions, which are commonly used to model and describe the variability of a variable. There is a difference between dependent and independent variables, with dependent variables being affected by other variables. Normal distributions can be used in scientific research to analyze data, make predictions, and test hypotheses.
  • #1
ebrattr
17
0
Hi everyone,
I would like to know if this stament is true or not. I have two variables [itex]u,v[/itex] both of them distributed as normal distribution with mean 0 and variance [itex]a^2[/itex]. Is it true that the expected value of [itex]uv[/itex] is [itex]a^2[/itex] ?
Thanks
 
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  • #2
If u and v are independent, this is not true.
Just consider the symmetry of the system.
 
  • #3
Yeahhh... its cero. Thanks.
 

1. What is a variable?

A variable is a quantity or characteristic that can take on different values in a given situation or experiment. It is typically denoted by a letter or symbol and can be either numerical (quantitative) or categorical (qualitative).

2. How are variables related to normal distributions?

Normal distributions, also known as Gaussian distributions, are a type of probability distribution that are commonly used to model and describe the variability of a particular variable. In a normal distribution, the majority of observations cluster around the mean value, with fewer observations occurring at the extremes.

3. What is the difference between a dependent and independent variable?

A dependent variable is a variable that is being measured or observed and is expected to change depending on the values of other variables, known as independent variables. Independent variables, on the other hand, are not affected by other variables and are used to explain or predict changes in the dependent variable.

4. How do you determine if a variable is normally distributed?

A variable is considered to be normally distributed if the majority of its values fall around the mean, with fewer values at the extremes. This can be visually assessed using a histogram or quantitatively assessed using statistical tests such as the Shapiro-Wilk test or the Kolmogorov-Smirnov test.

5. How can normal distributions be used in scientific research?

Normal distributions are commonly used in scientific research to analyze and describe data, make predictions, and test hypotheses. They can also be used to determine the likelihood of obtaining a certain result or to compare groups or populations.

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