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Problem Statement: We are given two Gaussian random variables, X1 and X2, with means m1 and m2, and variances v1 and v2 respectively. We know that the sum X1+X2=n. We need to determine the expected value of X2.
Understanding the Problem:
Key Concept: Linearity of Expectation
Solution:
Setup the Equation:
Solve for E[X2]:
Explanation:
Conclusion:
Note: