Question:

Let 𝑋1, 𝑋2, 𝑋3 be a random sample from an 𝑁(πœƒ, 1) distribution, where πœƒ ∈ ℝ is an unknown parameter. Then, which one of the following conditional expectations does NOT depend on πœƒ ?

Updated On: Oct 1, 2024
  • 𝐸(𝑋1+𝑋2βˆ’π‘‹3 | 𝑋1 + 𝑋2)
  • 𝐸(𝑋1 + 𝑋2 βˆ’ 𝑋3 | 𝑋2 + 𝑋3)
  • 𝐸(𝑋1 + 𝑋2 βˆ’ 𝑋3 | 𝑋1 βˆ’ 𝑋3)
  • 𝐸(𝑋1 + 𝑋2 βˆ’ 𝑋3 | 𝑋1 + 𝑋2 + 𝑋3)
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The Correct Option is D

Solution and Explanation

The correct option is (D): 𝐸(𝑋1 + 𝑋2 βˆ’ 𝑋3 | 𝑋1 + 𝑋2 + 𝑋3)
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