Correct answer: (A) φ_X(a)=1; (B) φ_X is periodic with period a.
Explanation
Write X=2πK/a for an integer K. Then e^(iaX)=1 almost surely,so φ(a)=1 and φ(t+a)=φ(t). C fails at t=0 (and every integer multiple of a). D uses incompatible inversion frequency,interval and normalization;the correct formula is P(X=2πn/a)=(1/a)∫₀^a e^(−i2πnt/a)φ_X(t)dt. **A,B**.
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