MT #7 is a Maple Assignment [This needs to be handed in.]
(You can use maple or web-maple (with pdf mode))
MT #7 is due Thursday 18 Oct 2001

Papers which are not STAPLED will not be acepted
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

All plots need to have a title which includes your name, (eventually plots
might have multiple functions and plots with mulitple functions need legends.)
Be sure to answer the questions as Maple comments. One can add
titles to plots like
 plot(sin(x),x=0..2*Pi,title="Catch the Wave");

Introduction to Syntax. Note often the expressions below are not given
in a format exceptable to Maple. For example, Maple does not understand
3x as 3*x, one must enter 3*x. Maple uses Pi for pi and does not know 
about e (either use exp(x) for e^x, or define e:=exp(1) before using it).

Typing ?diff into webmaple will give you help on the the diff command

Do the following using maple 
0. Enter your name(s) as an assignment statement like MyName:="Jane Doe";
or OurNames:="Gwyneth Paltrow and Ben Affleck";
1-3. Use the following two things:
A. Define bell (the bell shape curve) to be the maple expresssion [has a typo]
exp(-(x-mu)^2/(2*sigma^2))/(sigma*sqrt(2*Pi). [mu is the mean and sigma
is the standard deviation.]
B. If 25 Calculus 2 students take a test with density function rho(x),
the number of students expected to get a score between 80 and 90 is
25 times int(rho,x=80..90). (We want decimals, so you need to evalf too.)
1. Using bell (above) and subs, create the density bellm75s15 with
mean 75 and standard deviation 15. Use it to find the expected number
of students with scores in the six ranges: 90-100, 80-90, 70-80, 60-70
50-60 and 0-50. MAKE SURE YOUR ANSWERS ARE DECIMALS, and not in terms
of the error function erf.
2. Repeat problem #1 for both bellm75s10 (mean 75, standard deviation 10)
and bellm70s15 (mean 70, standard deviation 15).
3. Of course the bell shape curve is only an approximation. For the
three bells in 1&2 find both the number of students expected with
scores <= 0 and expected with scores >= 100. Again decimals and not erf.
4. Let c>0, use Maple to show the mean of the density (for x>0)
rho=ce^-cx is 1/c, the median of rho is ln(2)/c. And find the T,
where (N-1)/N is the probability of x being less than or equal to T.
5. Lets put two graphs side by side again. One the left plot we want
probability densities. f is c*e^-cx where c = 1/4, g is the bell
shape curve with mu=5, sigma=1 and h is the bell shape curve with
mu=7 and sigma=3. Use
the range 0..15, titles and legends and linestyles. On the right
plot do the cumulative distribution functions for these densities,
also over 0..15, with titles and legends and linestyles and stuff.]
[Careful, f is 0 for x < 0, so the distribution integral starts at
zero instead of -infinity.]

[How to get 2 plots on the same webmaple: 1st you need `with(plots):'
(you can use the `:' to surpress the output, or you can use the `;'
and see all the functions. You create two plots assigning them each
a name like F:=plot(sin(x),x=0..2*Pi): and G:=plot(cos(x),x=0..2*Pi):.
Now here the `:' is more important. If you leave off you will get
about a page of meaningless output. (Well it has meaning and contains
a list of the points plotted, but I don't want to see this on your
answer sheets. Neither of the assignments will produce a picture, but
the command `display(array([F,G]));' will. Careful `display([F,G])'
will combine the two plots into one and if the scales are not close
you might only see one of the graphs.]