1.Let be standard normal random variable. Let

a)(4 points.) What is the median of ?

b)(4 points.) What is ?

c)(4 points.) What is the 0.95-quantile of ?

Notes for this problem (#5):

You could use R to find the probability or quantiles of a distribution. It is also fine to use simulation to check your answers. However, using simulation only for an approximate answer will receive point deduction.

You are NOT supposed to search online what kind of random variable Y is. You did not learn this specific random variable in this class, and you do not need that information to solve this problem.