Exercise Solution 3.48

  1. By [3.219]

    [s1]

    [s2]

    By [3.218] and [3.220]

  2. [s3]

    [s4]

    By [3.217]

    [s5]

    [s6]

    [s7]

  3. The square of a standard normal random variable is chi-squared. Specifically

    [s8]

    By [3.220]

    [s9]

    By [3.217]

    [s10]

    [s11]

    [s12]