Question:

Let 𝑋1, 𝑋2, be a sequence of 𝑖.𝑖.𝑑. random variables each having π‘ˆ(0,1) distribution. Let π‘Œ be a random variable having the distribution function 𝐺. Suppose that
\(lim𝑛_{nβ†’βˆž} \frac{( 𝑋-1+𝑋_2+𝑋_𝑛}{4} ≀ π‘₯)=𝐺(π‘₯)\), for all π‘₯ ∈ ℝ . 
Then, π‘‰π‘Žπ‘Ÿ(π‘Œ) equals

Updated On: Oct 1, 2024
  • \(\frac{1}{12}\)
  • \(\frac{1}{32}\)
  • \(\frac{1}{48}\)
  • \(\frac{1}{64}\)
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The Correct Option is D

Solution and Explanation

The correct option is (D): \(\frac{1}{64}\)
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