Skip to main content
Statistics LibreTexts

4.S: Random Variables (Solutions- Practice + Homework)

  • Page ID
    5559
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    \( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)

    ( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\id}{\mathrm{id}}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\kernel}{\mathrm{null}\,}\)

    \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\)

    \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\)

    \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    \( \newcommand{\vectorA}[1]{\vec{#1}}      % arrow\)

    \( \newcommand{\vectorAt}[1]{\vec{\text{#1}}}      % arrow\)

    \( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vectorC}[1]{\textbf{#1}} \)

    \( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)

    \( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)

    \( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)

    \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    1.

    \(x\) \(P(x)\)
    0 0.12
    1 0.18
    2 0.30
    3 0.15
    4 0.10
    5 0.10
    6 0.05
    Table \(\PageIndex{6}\)

    3.

    0.10 + 0.05 = 0.15

    5.

    1

    7.

    0.35 + 0.40 + 0.10 = 0.85

    9.

    1(0.15) + 2(0.35) + 3(0.40) + 4(0.10) = 0.15 + 0.70 + 1.20 + 0.40 = 2.45

    11.

    \(x\) \(P(x)\)
    0 0.03
    1 0.04
    2 0.08
    3 0.85
    Table \(\PageIndex{7}\)

    13.

    Let \(X =\) the number of events Javier volunteers for each month.

    15.

    \(x\) \(P(x)\)
    0 0.05
    1 0.05
    2 0.10
    3 0.20
    4 0.25
    5 0.35
    Table \(\PageIndex{8}\)

    17.

    1 – 0.05 = 0.95

    18.

    \(X =\) the number of business majors in the sample.

    19.

    2, 3, 4, 5, 6, 7, 8, 9

    20.

    \(X =\) the number that reply “yes”

    22.

    0, 1, 2, 3, 4, 5, 6, 7, 8

    24.

    5.7

    26.

    0.4151

    28.

    \(X =\) the number of freshmen selected from the study until one replied "yes" that same-sex couples should have the right to legal marital status.

    30.

    1,2,…

    32.

    1.4

    35.

    0, 1, 2, 3, 4, …

    37.

    0.0485

    39.

    0.0214

    41.

    \(X =\) the number of U.S. teens who die from motor vehicle injuries per day.

    43.

    0, 1, 2, 3, 4, ...

    45.

    No

    48.

    1. 50.
      1. 53.

        \(X =\) the number of patients calling in claiming to have the flu, who actually have the flu.

        55.

        0.0165

        57.

        1. 59.

          4. 4.43

          4

          63.

          • 65.
            1. 67.
              1. 69.
                1. 71.
                  1. 73.
                    1. Figure \(\PageIndex{4}\)
                    2. 75.
                      1. 77.
                        1. 79.

                          0, 1, 2, and 3

                          1. 82.
                            1. 84.

                              Let \(X =\) the number of defective bulbs in a string.

                              • Using the binomial distribution:
                                • The Poisson approximation is very good—the difference between the probabilities is only \(0.0026\).

                                  86.

                                  1. 88.
                                    1. 90.
                                      1. 92.
                                        1. 94.

                                          4


    This page titled 4.S: Random Variables (Solutions- Practice + Homework) is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.