# Exercise Solution 3.4

In the following solution, ϕ_{Z} denotes the PDF of *Z*.

- By [3.6],
[s1]

[s2]

[s3]

[s4]

[s5]

[s6]

- By [3.6] and [3.7],
[s7]

[s8]

[s9]

[s10]

[s11]

[s12]

[s13]

[s14]

- The standard deviation of a random variable is simply the square root of its variance:
[s15]