Let X∼N(0,σ2)X \sim N(0, \sigma^2)X∼N(0,σ2). Find the expected value of the random variable Y=∣X∣3Y = |X|^3Y=∣X∣3.
2σ32π2\sigma^3 \sqrt{\frac{2}{\pi}}2σ3π2
σ32π\sigma^3 \sqrt{\frac{2}{\pi}}σ3π2
3σ32π3\sigma^3 \sqrt{2\pi}3σ32π
3σ33\sigma^33σ3