Find mean and variance of X and Y

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SUMMARY

The discussion focuses on calculating the mean, variance, and correlation coefficient for random variables X and Y based on their marginal distributions derived from a table. The correct formula for the mean of a random variable is emphasized as βX = ∑ x_i P_X(x_i), where x_i represents the values of X and P_X(x_i) denotes their respective probabilities. The user initially miscalculated the means for X and Y, indicating a need for clarity on the definitions and calculations involved in statistical analysis.

PREREQUISITES
  • Understanding of marginal distributions
  • Knowledge of probability theory
  • Familiarity with statistical formulas for mean and variance
  • Basic skills in manual calculations of statistics
NEXT STEPS
  • Study the calculation of variance for random variables
  • Learn about the correlation coefficient and its significance
  • Explore the concept of joint distributions and their applications
  • Review statistical software tools for calculating mean and variance, such as R or Python's NumPy library
USEFUL FOR

Students in statistics, data analysts, and anyone involved in statistical computations who seeks to understand the foundational concepts of mean, variance, and correlation in probability distributions.

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Homework Statement



I have found the marginal distribution for X and Y from a table. (No statistical regression, just simple table)
How should I proceed in finding mean, variance an correlation coefficient of X and y? I am computing by hand.
Thank you,



Homework Equations





The Attempt at a Solution

 

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Is mean for X:

(1/8+3/8+3/8+1/8)
-------------------
4

and mean for Y is

(2/8+4/8+2/8)
--------------
3

?
 
No. Remember the mean of a random variable is defined as

\bar{X} = \sum_i x_i P_X(x_i)

It's the sum of the product of the values X can take on multiplied by probability of that value.
 

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