Math Is Fun Forum

Well I have problem understanding this question as I don't even know where to start. Would appreciate if anyone could sheath some light on how to tackle this question or at least give some hint on where to start.

The Z Corporation issues a 10%, 20-year bond at a time when yields are 10%. The bond has a call provision that allows the corporation to force a bond holder to redeem his or her bond at face value plus 5%. After 5 years the corporation finds that exercise of this call provision is advantageous. What can you deduce about the yield at that time? (Assume one coupon payment per year.)

Well, there is a corollary on Maximum Modulus Principle that goes like this:

"If

is analytic on a path connected open set

and

attains its maximum value at a point

in

, then

is constant on

."

Well my question are:

1.)Does this statement holds true if I replace "maximum" with "minimum"?

2.)More generally, does Maximum Modulus Principle and all its corollaries the same as Minimum Modulus Principle just that we only have to replace the word "maximum" with "minimum"?

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3.) Alright this question is not on Maximum Modulus Principle, it's something regarding the phrasing of Mathematics that I am confused in.

Let's say if we say something like

lies in

is it the same as saying

lies on

?

and the same goes for if

lies in

is it the same as saying

lies on

?

I am asking this because I always though if we say something lie in something such as 

we mean that it is contain inside the circle. Whereas when we say something lies on

, we actually mean that it "sit" right on the circumference of the circle or sometime refer to as

.

However, it seem to me that some textbook just use them interchangeable, could any kind soul confirm this for me?

Thanks and will appreciate if anyone could answer my questions as my exam on Complex Analysis is on next week

Hi, may I know the degree of freedom for a chi-squared test? What is given on my notes is k-p-1 where k denote the no. of classes, p denote estimated parameter. However this is one question that really confused me:

30 passengers on a flight took part in an experiment to investigate if a new drug suppresses jet lag. The subjects were divided into two group, one given the course of treatment and the other was given a placebo.

                                   Jet lag                 No jet lag
Treatment group             3                           12
Placebo group                 10                         5

With data above, use a chi-squared test to investigate if the treatment suppressed jet lag.

Solution is given as:

There is no association between experiencing jet lag and the treatment

Treatment suppressed jet lag

The expected frequencies are as follows:

                                  Jet lag                 No jet lag
Treatment group             6.5                        8.5
Placebo group                 6.5                        8.5

Hence the test statistic is:

Degree of freedom:

.
.
.
.

My question is, why is the degree of freedom (2-1)(2-1)=1 ? Isn't it 4-1=3? since no. of classes is 4 and there are no estimated parameter?

Thanks a bunch in advance, I have an exam this week.