If X∼Exponential(λ)X \sim \text{Exponential}(\lambda)X∼Exponential(λ), what is the variance of Y=XY = \sqrt{X}Y=X?
1λ(1−π4)\frac{1}{\lambda} (1 - \frac{\pi}{4})λ1(1−4π)
14λ\frac{1}{4\lambda}4λ1
1λ2\frac{1}{\lambda^2}λ21
1λ(1−14)\frac{1}{\lambda} (1 - \frac{1}{4})λ1(1−41)