4. Give short answers to the following questions.
i. What are the mean and standard deviation of Po(1.5), the Poisson distribution with
parameter \(\lambda = 1.5\)?
ii. Suppose that the random variable X follows the normal distribution N(2, 0.5). Define
a random variable Y, which depends on X, such that Y will follow the standard normal
distribution N(0, 1).
iii. Use a parameter of the standard normal distribution N(0, 1) to write down the answer
of \(\frac{1}{\sqrt{2\pi}} \int_{-\infty}^{\infty} z^2 e^{-\frac{z^2}{2}} dz\).
iv. Use a property of the standard normal distribution N(0, 1) to write down the answer
of \(\frac{1}{\sqrt{2\pi}} \int_{0}^{\infty} e^{-\frac{z^2}{2}} dz\).
