Mathematics · Probability Theory
Let X and Y be real-valued independent random variables. Which of the following statements is always correct for all t, u ∈ ℝ?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1P({X = a} ∪ {Y = b}) = P({X = a})P({Y = b}) for all a, b ∈ ℝ
- 2{X = a} ∩ {Y = b} = ∅ for all a, b ∈ ℝ
- 3If X ~ N(2, 1) and Y ~ N(0, 2), then Var(X + Y) = 1
- 4E[cos(tX + uY)] = E[cos(tX)]E[cos(uY)] - E[sin(tX)]E[sin(uY)]✓
Correct answer
E[cos(tX + uY)] = E[cos(tX)]E[cos(uY)] - E[sin(tX)]E[sin(uY)]
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