Let $ X $ and $ Y $ be independent random variables having $ \text{Bin}(18, 0.5) $ and $ \text{Bin}(20, 0.5) $ distributions, respectively. Further, let $ U = \min\{X, Y\} $ and $ V = \max\{X, Y\} $. Then which of the following statements is/are correct?

Question

cdquestions Admin · Accepted Answer

The correct option is (A): $ E(U + V) = 19 $,(B): $ E(|X - Y|) = E(V - U) $ ,(D): $ 38 - (X + Y) $ has $ \text{Bin}(38, 0.5) $ distribution

Answer

$ E(U + V) = 19 $

Answer

$ E(|X - Y|) = E(V - U) $

Answer

$ \text{Var}(U + V) = 16 $

Answer

$ 38 - (X + Y) $ has $ \text{Bin}(38, 0.5) $ distribution

Let \( X \) and \( Y \) be independent random variables having \( \text{Bin}(18, 0.5) \) and \( \text{Bin}(20, 0.5) \) distributions, respectively. Further, let \( U = \min\{X, Y\} \) and \( V = \max\{X, Y\} \). Then which of the following statements is/are correct?

The Correct Option is A, B, D

Solution and Explanation

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