Assignment: Read section 1.1 and 1.2. Do section 1.1 problems 1,2,11,12,17. (If you can't get your computer to do the simulations write down carefully what you are trying to tell the computer to do, and we'll work out the bugs later as we become more comfortable with programing in maple.)
Comments: The computer demos and experiments we are using in class can be found here: Computer Demos.
Wednesday
Assignment: Please read section 1.2 and 2.1. Do problems in section 1.2 do problems 4,5,11,14,17,18,19,31.
Comments: Today and Friday we will cover section 1.2. It is worth noting that the definitions and ideas presented in class will be a balance between the intuitive friendly definitions in the book and the harsh definitions found in more advanced treatments of probability. We will discuss in next week's x-session why there are different approaches and the history of these approaches.
Friday
Assignment: In section 1.2 do problems 20,21,23,28 in section 2.1 do problem 3. Read sections 2.1 and 2.2.
Comments: Here is my maple code for problem 17 from the first assignment. I apologize that it is a bit ugly to look at, but it should be a nice template for adding some graphics to your own code.
Walk1d := proc(n)
local i, ran, position, positionlist,walk;
with(plottools):
position := 0;
positionlist :=[[0,0]];
for i from 0 to n
do
if position = 0 then
lprint(`Im home at step ` , i , ``);
fi;
ran := rand(1..2)();
if ran = 1 then
position := position + 1;
else
position := position - 1 ;
fi;
positionlist := [op(positionlist),[i,position]];
od;
lprint(`my final position is `, position,``);
lprint(`Here is a graph of my random adventure in one dimension, viewed
with "time" as the x-axis.`);
walk := curve(positionlist,color=red,thickness =1 );
plots[display](walk);
end:
Walk1d(1000);
with(plottools):
Walk2d := proc(n,show)
local i, ran, positionx, positiony, positionlist,walk,list3,walk3;
with(plottools):
positionlist := [[0,0]];
list3 := [[0,0,0]];
positionx := 0;
positiony := 0;
for i from 0 to n
do
if positionx = 0 and positiony = 0 then
lprint(`Im home at step ` , i , ``);
fi;
ran := rand(1..4)();
if ran = 1 then
positionx := positionx + 1;
fi;
if ran = 2 then
positionx := positionx - 1 ;
fi;
if ran = 3 then
positiony := positiony + 1 ;
fi;
if ran = 4 then
positiony := positiony - 1 ;
fi;
positionlist := [op(positionlist),[positionx,positiony]];
list3 := [op(list3),[positionx,positiony,i]];
od;
lprint(`my final position is `, [positionx , positiony],``);
if show then
lprint(`Here is a graph of my random adventure in two dimensinos.`);
walk := curve(positionlist,color=green,thickness =2 );
plots[display](walk);
else
lprint(`Here is the walk vied over time, with time as the z axis.`);
walk3 := curve(list3);
plots[display](walk3,orientation=[0,0],axes=box,thickness=2);
fi;
end:
Walk2d(1000,true);
Walk2d(1000,false);
Walk3d := proc(n)
local i, ran, positionx, positiony , positionz, positionlist,walk;
with(plottools):
positionx := 0;
positiony := 0;
positionz := 0;
positionlist :=[[0,0,0]];
for i from 0 to n
do
if positionx = 0 and positiony = 0 and positionz = 0 then
lprint(`Im home at step` , i , ``);
fi;
ran := rand(1..6)();
if ran = 1 then
positionx := positionx + 1;
fi;
if ran = 2 then
positionx := positionx - 1 ;
fi;
if ran = 3 then
positiony := positiony + 1 ;
fi;
if ran = 4 then
positiony := positiony - 1 ;
fi;
if ran = 5 then
positionz := positionz + 1 ;
fi;
if ran = 6 then
positionz := positionz - 1 ;
fi;
positionlist := [op(positionlist),[positionx,positiony,positionz]];
od;
lprint(`my final position is `, [positionx , positiony,positionz], ``);
lprint(`Here is a graph of my random adventure in three dimensions.`);
walk := curve(positionlist,thickness=2);
plots[display](walk);
end:
Walk3d(1000);