Mathematics · Probability Theory
Let (Xn, n ≥ 1) and X be random variables defined on a common probability space, all having finite expectation and having characteristic functions (φn, n ≥ 1) and φ respectively. Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1If φn(t) → φ(t) for all t, then Xn(ω) → X(ω) for at least one sample point ω
- 2If Xn(ω) → X(ω) for every sample point ω, then φn(t) → φ(t) for all t✓
- 3If Xn(ω) → X(ω) for every sample point ω, then E(Xn) → E(X)
- 4If E(Xn) → E(X), then there is at least one sample point ω such that Xn(ω) → X(ω)
Correct answer
If Xn(ω) → X(ω) for every sample point ω, then φn(t) → φ(t) for all t
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