Conditional expectations of bivariate normal distributions

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SUMMARY

The discussion focuses on solving problems related to conditional expectations in bivariate normal distributions, specifically for random variables X and Y with means m_X = m_Y = 0 and standard deviations σ_X = σ_Y = 1. The key tasks include calculating E(X|Y=1) and Var(X|Y=1), as well as determining the probability Pr(X+Y>0.5). The joint density function is a crucial component for these calculations, as referenced in the provided link to MathWorld's Bivariate Normal Distribution.

PREREQUISITES
  • Bivariate normal distribution concepts
  • Conditional expectation and variance calculations
  • Joint density functions
  • Probability theory fundamentals
NEXT STEPS
  • Study the properties of bivariate normal distributions
  • Learn how to compute conditional expectations and variances
  • Explore joint density functions in detail
  • Investigate probability calculations involving sums of random variables
USEFUL FOR

Students in statistics, data analysts, and anyone working with bivariate normal distributions seeking to enhance their understanding of conditional expectations and variance calculations.

Ryuuzakie
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Hey guys, I'm having a bit of a problem with this question...


Homework Statement


If X and Y have a bivariate normal distribution with m_X=m_y=0 and \sigma_X=\sigma_Y=1, find:

a) E(X|Y=1) and Var(X|Y=1)
b) Pr(X+Y>0.5)


Homework Equations


N/A


The Attempt at a Solution


Apologies, but I don't seem to know where to start on this one.
 
Physics news on Phys.org
how about the joint denisty function?
 

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