yikes!
--
Richard E. Hawkins, Asst. Prof. of Economics /"\ ASCII ribbon campaign
[EMAIL PROTECTED] Smeal 178 (814) 375-4700 \ / against HTML mail
These opinions will not be those of X and postings.
Penn State until it pays my retainer. / \
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\layout Title
Probability
\layout Author
Prof.
Hawkins
\layout Date
Due: June 19, MMI, Noon
\layout Standard
5 points.
Your report should be typed and in a coherent format.
\layout Standard
Recall the example in class where we each rolled three dice, and calculated
the mean.
This continues from there.
\layout Enumerate
For a single roll of
\begin_inset Formula \( 1d6 \)
\end_inset
, what is the
\begin_deeper
\layout Enumerate
expected value
\layout Enumerate
the variance?
\end_deeper
\layout Enumerate
\begin_inset LatexCommand \label{makeRolls}
\end_inset
Make a table with the results of
\begin_inset Formula \( 36 \)
\end_inset
rolls.
\begin_deeper
\layout Enumerate
Calculate your sample mean.
\layout Enumerate
Calculate your sample variance.
\layout Enumerate
Make a histogram of the individual rolls
\end_deeper
\layout Enumerate
How do your results in
\begin_inset LatexCommand \ref{makeRolls}
\end_inset
compare to what you expected? Be specific.
\layout Enumerate
Using a spreadsheet or Minitab, draw
\begin_inset Formula \( 100 \)
\end_inset
samples of
\begin_inset Formula \( 49 \)
\end_inset
observations each.
Calculate the mean for each of your samples.
In a spreadsheet, a random number from
\begin_inset Formula \( 1 \)
\end_inset
to
\begin_inset Formula \( n \)
\end_inset
can be created by the equation
\begin_inset Formula \( =int\left( n*rand()\right) +1 \)
\end_inset
(In current versions of excel, you may use
\begin_inset Formula \( rand\_between(1,n) \)
\end_inset
to obtain an integer from
\begin_inset Formula \( 1 \)
\end_inset
to
\begin_inset Formula \( n \)
\end_inset
if you have appropriate modules installed).
The
\begin_inset Formula \( rand() \)
\end_inset
returns a variable between
\begin_inset Formula \( 0 \)
\end_inset
and
\begin_inset Formula \( 1 \)
\end_inset
, the
\begin_inset Formula \( n \)
\end_inset
scales it, the
\begin_inset Formula \( int \)
\end_inset
turns it into the next lowest integer, and the
\begin_inset Formula \( +1 \)
\end_inset
shifts it so the minimum value is
\begin_inset Formula \( 1 \)
\end_inset
rather than
\begin_inset Formula \( 0 \)
\end_inset
.
\layout Enumerate
Make a histogram of your sample means.
\layout Enumerate
Download the data from
\latex latex
\latex default
http://www.personal.psu.edu/reh18/stat200/lab2.xls
\latex latex
\begin_deeper
\layout Enumerate
Calculate
\begin_deeper
\layout Enumerate
the mean
\layout Enumerate
the median
\layout Enumerate
the mode
\layout Enumerate
the variance
\layout Enumerate
the standard deviation
\end_deeper
\layout Enumerate
make a histogram
\layout Enumerate
what might have produced this data?
\layout LaTeX
\backslash
pagebreak
\end_deeper
\layout Enumerate
Let the following definitions hold:
\begin_deeper
\layout Standard
\begin_inset Formula \( A\equiv \left\{ 1,3,5,7,9\right\} \)
\end_inset
\layout Standard
\begin_inset Formula \( B\equiv \left\{ 2,4,6,8\right\} \)
\end_inset
\layout Standard
\begin_inset Formula \( C\equiv \left\{ 3,5,8,9\right\} \)
\end_inset
\layout Standard
\begin_inset Formula \( D\equiv \left\{ 2,4\right\} \)
\end_inset
\layout Standard
\begin_inset Formula \( E\equiv \left\{ 7\right\} \)
\end_inset
\layout Enumerate
what is
\begin_inset Formula \( S \)
\end_inset
, the universal set?
\begin_deeper
\layout LaTeX
\backslash
vskip .5in
\end_deeper
\layout Enumerate
what is
\begin_inset Formula \( D\cap E \)
\end_inset
\begin_deeper
\layout LaTeX
\backslash
vskip .5in
\end_deeper
\layout Enumerate
what is
\begin_inset Formula \( \bar{C} \)
\end_inset
\begin_deeper
\layout LaTeX
\backslash
vskip .5in
\end_deeper
\layout Enumerate
What is
\begin_inset Formula \( E/A \)
\end_inset
\begin_deeper
\layout LaTeX
\backslash
vskip .5in
\end_deeper
\layout Enumerate
what is
\begin_inset Formula \( D\cup C \)
\end_inset
\begin_deeper
\layout LaTeX
\backslash
vskip .5in
\end_deeper
\layout Enumerate
of what set or sets is
\begin_inset Formula \( C \)
\end_inset
a subset?
\begin_deeper
\layout LaTeX
\backslash
vskip .5in
\end_deeper
\layout Enumerate
of what set or sets is
\begin_inset Formula \( A \)
\end_inset
a superset?
\end_deeper
\layout LaTeX
\the_end
