A continuous random variable has probability density function for , and otherwise. Find the expectation .
Answer and explanation
Correct answer: D.
- Step 1: Compute the expectation using .
- Step 2: Evaluate the definite integral: . Multiply by the prefactor: .
Answer
.
Why not the others: The fraction incorrectly assumes a symmetric uniform distribution on ; the fraction forgets the denominator factor 2 in the integral result; the fraction makes an arithmetic error evaluating .
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