Exercise Solution 3.4

In the following solution, ϕZ denotes the PDF of Z.

  1. By [3.6],

    [s1]

    [s2]

    [s3]

    [s4]

    [s5]

    [s6]

  2. By [3.6] and [3.7],

    [s7]

    [s8]

    [s9]

    [s10]

    [s11]

    [s12]

    [s13]

    [s14]

  3. The standard deviation of a random variable is simply the square root of its variance:

    [s15]

 

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