5.5: Exercises
- Last updated
- Jun 6, 2021
- Save as PDF
\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}}}
\newcommand{\avec}{\mathbf a} \newcommand{\bvec}{\mathbf b} \newcommand{\cvec}{\mathbf c} \newcommand{\dvec}{\mathbf d} \newcommand{\dtil}{\widetilde{\mathbf d}} \newcommand{\evec}{\mathbf e} \newcommand{\fvec}{\mathbf f} \newcommand{\nvec}{\mathbf n} \newcommand{\pvec}{\mathbf p} \newcommand{\qvec}{\mathbf q} \newcommand{\svec}{\mathbf s} \newcommand{\tvec}{\mathbf t} \newcommand{\uvec}{\mathbf u} \newcommand{\vvec}{\mathbf v} \newcommand{\wvec}{\mathbf w} \newcommand{\xvec}{\mathbf x} \newcommand{\yvec}{\mathbf y} \newcommand{\zvec}{\mathbf z} \newcommand{\rvec}{\mathbf r} \newcommand{\mvec}{\mathbf m} \newcommand{\zerovec}{\mathbf 0} \newcommand{\onevec}{\mathbf 1} \newcommand{\real}{\mathbb R} \newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]} \newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]} \newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]} \newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]} \newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]} \newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]} \newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]} \newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]} \newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]} \newcommand{\laspan}[1]{\text{Span}\{#1\}} \newcommand{\bcal}{\cal B} \newcommand{\ccal}{\cal C} \newcommand{\scal}{\cal S} \newcommand{\wcal}{\cal W} \newcommand{\ecal}{\cal E} \newcommand{\coords}[2]{\left\{#1\right\}_{#2}} \newcommand{\gray}[1]{\color{gray}{#1}} \newcommand{\lgray}[1]{\color{lightgray}{#1}} \newcommand{\rank}{\operatorname{rank}} \newcommand{\row}{\text{Row}} \newcommand{\col}{\text{Col}} \renewcommand{\row}{\text{Row}} \newcommand{\nul}{\text{Nul}} \newcommand{\var}{\text{Var}} \newcommand{\corr}{\text{corr}} \newcommand{\len}[1]{\left|#1\right|} \newcommand{\bbar}{\overline{\bvec}} \newcommand{\bhat}{\widehat{\bvec}} \newcommand{\bperp}{\bvec^\perp} \newcommand{\xhat}{\widehat{\xvec}} \newcommand{\vhat}{\widehat{\vvec}} \newcommand{\uhat}{\widehat{\uvec}} \newcommand{\what}{\widehat{\wvec}} \newcommand{\Sighat}{\widehat{\Sigma}} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \definecolor{fillinmathshade}{gray}{0.9}Behavioral and ecological factors influence dispersion. Uniform patterns of dispersion are generally a result of interactions between individuals like competition and territoriality.
1. In ecology a uniform distribution of an organism may result when the organism exhibits territorial behavior that keeps most organisms. In one study, a portion of a field was divided into a 20 \times \20 grid and a count made of the number of organisms in each unit of the grid giving the results seen below.
| number of organisms in plot | frequency |
|---|---|
| 2 | 58 |
| 3 | 51 |
| 4 | 60 |
| 5 | 64 |
| 6 | 54 |
| 7 | 52 |
| 8 | 61 |
Create a plot similar to that in 5.4.1 and comment on your results.
2. Chlorine has two isotopes, 35Cl (75.8% abundance) and 37Cl (24.2% abundance). Create a plot similar to that in Figure 5.4.2 for the molecule PCB 77, a chlorinated compound with the formula C12H6Cl4 and comment on your results.
3. A radioactive decay process has a background level of 3 emissions per minute and follows a Poisson distribution. The number of emissions per minute was monitored for one hour giving the following results
| emissions per minute | frequency of event |
|---|---|
| 0 | 3 |
| 1 | 9 |
| 2 | 13 |
| 3 | 16 |
| 4 | 9 |
| 5 | 5 |
| 6 | 3 |
| 7 | 1 |
| 8 | 1 |
| 9 | 0 |
| 10 | 0 |
Use this data to create a plot similar to that in Figure 5.4.3 and comment on your results
4. Using the penny data from Exercise 3.4.5, create a plot similar to that in Figure 5.4.4 using all pennies minted after 1982 and comment on your results.
5. Use this link to access a case study on data analysis and complete the first four investigations included in Part IV: Ways to Model Data.
