Math Forum / Mathematics / Recreational Math / November 2004

Is there a site or PDF file on the web which shows how you use the Chage
Of Variable technique in probability
theory?  The one where you use the Jacobian transformation to obtain a
probability density function.

"I can teach anyone how to get what they want out of life. The problem is I can't find anybody who can tell me what they want." -- Mark Twain "Today people in America can become whatever they want. Trouble is most don't know what they want." -- Earl Nightingale What do you want? ...

My submission as reason #10
A six-pack will have ten bottles of beer!  Woo hoo!

   I'm building an Acceleration Sensor for a Model Rocket that I'd
like to calibrate it by spinning around on a string.  Seems to me that
if I know the Rate of Spin and the Length of the String, then I should
be able to calculate the Centrifugal Force (Lateral Acceleration.)

We have a string of bowls b_0, b_1, b_2, b_3, and so on. Counters are
placed into bowls b_1, b_2, b_3,... All the counters have to finish in
bowl 0 (b_0) according to the following rule. If there are 3 counters
in bowl 3 (b_3) then we can move them by putting one of them in bowl

Assume we have a perfect clock with hour, minute, and second hands.
Beginning at 12:00, when all three hands are on the 12, how many
times will the three hands be exactly 120 degrees apart before all
three hands are again on the 12?

Help!
My buddy gave me this problem to torment me. Needless to say, I'm lost.
Please help:
The lives of a certain brand of nine-volt batteries are normally

I've got a flat plate in a pipe that is 30 degrees off perpendicular.  How
can I calculate the area of the plate?  Two things (I think) I know are:  1)
the flat plate is now 1 / 0.866 times longer than if it were a circular
(perpendicular to the pipe); and 2) the formula for an ...

I am trying to construct a transformation matrix that has an origin shift.
It has the following mappings,
(x, y)
(0, 0) -> (0, b)

Given a number n, is there a tight upper bound on the number of its
distinct factors (need NOT be prime), d(n)?
Specifically, is d(n) = O(logn)?
Thanks for any help,

The product of 2 numbers is 108. The smaller number is 3 less than 1/2
the larger number. What are the 2 numbers. I get a basic equation such
as:
x times (.5x)-3 = 108. Then I'm lost as to how to go from there. Can

Conjecture 1- (Euler). It's impossible to express a fifth
                       power as a sum of four perfect fifth powers.
I am interested to prove or disprove following assertion :
Conjecture 2. If  a<b<c<d<e  are positive integers satisfying    

Anyone interested in discussing the pros and cons of an alternative
number base system and its application to teaching of maths and our
weights and measures. The system in question would use 12 as a number
base.

Okay, I have a partial (or should I say fractional?) understanding of
Fractional Calculus. Taking the 1/2 derivative of a function seems
pretty strange no matter how I look at it though.
Does anyone know what - if any - real world applications have been found

If you compute something like 5**(3/11), you can either compute the 11
roots of 5**(1/11) and then cube them all, or you can cube 5 and then
compute the 11 roots of 125**(1/11). The order is invariant.
This seems obvious when you take X**(m/n) where m/n is reduced to