Consider a random variable \(X\) with mean \(\mu\) and standard deviation \(\sigma\). Define a new random variable \(Y\) by

\[Y=\frac{X-\mu}{\sigma}\,.\]

- Show that \(Y\) has mean 0 and variance 1.
- Show that if \(a \) is some number \[\mathbf{P}( Y > a) = \mathbf{P}( X > \mu + a\sigma )\]