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# Search:

Type: Posts; User: ctperng; Keyword(s):

## Search: Search took 0.28 seconds.

by ctperng
Replies
3
Views
2,235

### I fixed the problem. The previous attempt assumed...

I fixed the problem. The previous attempt assumed that the given data formed a "probability distribution", but it DOES NOT. (That is why the variance led to false result.)

ctperng

by ctperng
Replies
3
Views
2,235

### Try this: ...

Try this:

E(X)=15*0.05+(15+20v)*0.95*0.1+(15+20v+25v^2)*0.95 *0.9
E(X^2)=15^2*0.05+(15+20v)^2*0.95*0.1+(15+20v+25v^2 )^2*0.95*0.9

ctperng

by ctperng
Replies
6
Views
2,624

### According to the question, at least two cars are...

According to the question, at least two cars are heart, so you should divide by the probability of getting (exactly two hearts and exactly three hearts).

ctperng
4. ## Thread: convolution S=x1 + x2 + x3

by ctperng
Replies
1
Views
1,840

### One way to do this is to use the Fourier...

One way to do this is to use the Fourier transform and inverse Fourier transform, using the fact that F(f*g) = F(f)F(g), where F is Fourier transform, and * is the convolution. This seems tedious,...
5. ## Thread: Exam C before MLC/MLF?

by ctperng
Replies
8
Views
4,409

### There is certainly no loss to trust you, but...

There is certainly no loss to trust you, but there is reason of his/her confusion: Exam C is now offered 3 times a year, if I read it correctly.
http://beanactuary.org/exams/cbt.cfm#dates

jk2ff:...

by ctperng
Replies
3
Views
2,209

### The deposit of money between t and t+dt is...

The deposit of money between t and t+dt is (8k+tk)dt = (8+t)kdt.

What would be the maturity value of this at then end of 10 years?

Answer: (8+t)kdt*e^{integral from t to 10 of delta(t)}, ...
7. ## Thread: can someone tell me what dist. to use?

by ctperng
Replies
10
Views
3,279

### You are absolutely right. The problem is how to...

You are absolutely right. The problem is how to interpret

"I get 12 calls per week evenly distributed."

If you fix the number of calls per week, and interpret even distributed as each call has...

by ctperng
Replies
10
Views
3,279

Thank you!
9. ## Thread: can someone tell me what dist. to use?

by ctperng
Replies
10
Views
3,279

### Interesting. Could you explain to me what you did...

Interesting. Could you explain to me what you did in your simulation? (PM is fine.)

To compute the probability of multinomial distribution, you could use exclusion-inclusion:

The probability...
10. ## Thread: Duration is boggling my mind

by ctperng
Replies
3
Views
1,938

### I believe in your calculation of P'(i)/P(i), you...

I believe in your calculation of P'(i)/P(i), you are thinking of i as effective interest rate. So when you want to multiply interest rate change with the duration, you should compute the difference...
11. ## Thread: Duration is boggling my mind

by ctperng
Replies
3
Views
1,938

### I like this: "I have gone back to first...

I like this: "I have gone back to first principles to find modified duration by finding P'(i)/P(i). "

According to my computation, this is about -3.61, and it contributes to the percentage price...
12. ## Thread: Proving analytically that probabilities of Negative Binomial sum to 1

by ctperng
Replies
2
Views
1,924

### As the previous post mentioned, your formula...

As the previous post mentioned, your formula doesn't seem to be right: your sum will be greater than 1.

Your question actually has been discussed in this forum:

See my posts
...
13. ## Thread: Force of interest

by ctperng
Replies
1
Views
1,808

### Hi, You just need to solve the following...

Hi,

You just need to solve the following equation for δ (which is a constant now):

100e^(10δ) + 100e^(5δ) = 316.45.

(Hint: letting x = e^(5δ), the equation is 100x^2 + 100x =316.45; once...

by ctperng
Replies
3
Views
2,613

### Thanks, nomoreexams. I was wondering if...

Thanks, nomoreexams.

I was wondering if Jensen's inequality and Cauchy-Schwarz's inequality (for real variables, of course) are equivalent for the special case f(x) = x^2. A moment's reflection...

by ctperng
Replies
3
Views
2,613

### Jensens inequality? (Well, I am not sure how one...

Jensens inequality? (Well, I am not sure how one solves this by it.)

But this can be easily solved by Cauchy-Schwarz's inequality:

(x^2 + 4y^2 + 9z^2)(1^2+(1/2)^2+(1/3)^2) >= (x + y + z)^2,...
16. ## Thread: one more complicated problem

by ctperng
Replies
3
Views
2,353

### For example, (number of choices of colors to...

For example, (number of choices of colors to apply on the 8 and 12 objects) = (12C4*8C4),

(number of ways to arrange objects for the colors) = (number of ways to arrange 8 objects on * * * *,...
17. ## Thread: one more complicated problem

by ctperng
Replies
3
Views
2,353

### These are some hints: Thinking of it as a...

These are some hints:

Thinking of it as a coloring problem: 12 colors applying on 20 objects; the total number of ways is 12^20.
Now for the desired outcomes, you need to pick 4 colors to apply...

by ctperng
Replies
7
Views
6,640

### If you make the following assumptions, then the...

If you make the following assumptions, then the numbers would match:

(1) each set calls exactly one repairer.
(2) each set calls the repairer ramdonly, and independently

When translated into...
19. ## Thread: Who wants to work out an equation for me?

by ctperng
Replies
22
Views
10,010

### = 0.022523*SQRT((H1-145)^2)...

= 0.022523*SQRT((H1-145)^2) -0.01752*SQRT((H1-700)^2) -0.0045*SQRT((H1-1000)^2) +0.003008*SQRT((H1-2000)^2) -0.00201*SQRT((H1-5000)^2) +0.0015*SQRT((H1-10000)^2) -0.0006*SQRT((H1-25000)^2)...
20. ## Thread: Who wants to work out an equation for me?

by ctperng
Replies
22
Views
10,010

### Not a problem. You can add the function...

Not a problem. You can add the function max(0,x-100000)*0.0028 to f(x), namely attach the following code to the Excel function above

+MAX(0,H1-100000)*0.0028

As for \$\$ concern, you look for...
21. ## Thread: Who wants to work out an equation for me?

by ctperng
Replies
22
Views
10,010

### You know what a function is, right? You can...

You know what a function is, right? You can consult with any person about how to input a function in a calculator which allows you to define your own function.

If your goal is just to compute, you...
22. ## Thread: Help - new to Actuarial Mathematics - 1st Exam Tomorrow

by ctperng
Replies
2
Views
1,804

### The concept you messed up is you are confused...

The concept you messed up is you are confused with annuity with definition of nominal interest rate.

Hope this clears up your confusion:

(1) (1+i(p)/p)^p = 1+i, this is definition of nominal...
23. ## Thread: Who wants to work out an equation for me?

by ctperng
Replies
22
Views
10,010

### Alright, if you solve the system of equations I...

Alright, if you solve the system of equations I mentioned earlier (either by hand or by using a calculator, say TI83 or TI84), you get the following numbers (there may be rounding error for the...
24. ## Thread: Who wants to work out an equation for me?

by ctperng
Replies
22
Views
10,010

### Right, I was being sloppy when I said it. But by...

Right, I was being sloppy when I said it. But by approximation, the error is at most 1. :)

ctperng
25. ## Thread: Who wants to work out an equation for me?

by ctperng
Replies
22
Views
10,010

### It is just approximation (very commonly used as...

It is just approximation (very commonly used as linear interpolation). Yes, this would get back to question about what he really wants. No big deal to me, i just want to show that something not too...
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