Let X∼N(μ,σ2)X \sim N(\mu, \sigma^2)X∼N(μ,σ2). Find the median of the transformed random variable Y=e2X−1Y = e^{2X - 1}Y=e2X−1.
e2μ−σ2−1e^{2\mu - \sigma^2 - 1}e2μ−σ2−1
e2μe^{2\mu}e2μ
e2μ−1e^{2\mu - 1}e2μ−1
e2μ+2σ2−1e^{2\mu + 2\sigma^2 - 1}e2μ+2σ2−1