Variables and normal distributions

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SUMMARY

The discussion centers on the relationship between two independent variables, u and v, both following a normal distribution with a mean of 0 and variance a². It is established that the expected value of the product uv is not a² when u and v are independent; rather, it is 0 due to the symmetry of the normal distribution. This conclusion is supported by the properties of independent normal variables.

PREREQUISITES
  • Understanding of normal distribution properties
  • Knowledge of expected value calculations
  • Familiarity with the concept of independence in statistics
  • Basic statistical terminology
NEXT STEPS
  • Study the properties of independent random variables
  • Learn about covariance and its implications for expected values
  • Explore the Central Limit Theorem and its applications
  • Investigate the implications of symmetry in probability distributions
USEFUL FOR

Statisticians, data analysts, and students studying probability theory who seek to deepen their understanding of normal distributions and their properties.

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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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If u and v are independent, this is not true.
Just consider the symmetry of the system.
 
Yeahhh... its cero. Thanks.
 

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