My Life Saver

POLO:

 Saving my life from sleeping in the class since Jun 2012.

(especially Elementary Stochastic Modelling class by Dr. T)

Surprising I get the highest coursework mark compared to all my subjects this semester.

Must be thanks to POLO.

In Setapak, this cost me about RM 0.55

In PJ, this cost me about RM 0.99 (Damn, saya ditipu!)

My study life (Week 10-14)

Almost 9 months I didn't draw any comics.
I don't think I am that busy and I always wonder what am I doing for the whole 9 months.
Whenever my friends asked me out, I will reject them. 

Maybe I will draw what happened from Week 1 to Week 9 next time.
But here what happened from Week 10 to Week 14.

(click on the picture to enlarge)

Probably I will need an ambulance very soon.
Anyone want to call 999 for me?

I hope I won't die before Final Exam.

Statisticians probably do it...

• Statisticians do it continuously but discretely.
• Statisticians do it when it counts.
• Statisticians do it with large numbers.
• Statisticians do it with significance.
• Statisticians do it on random walks.
• Statisticians do it stochastically.
• Statisticians do it. After all, it's only normal.
• Statisticians do it with standard deviations.
• Statisticians do it with 95% confidence.
• Statisticians do it with only a 5% chance of being rejected.

 Source:
http://jokelabs.com/humor_jokes-det-927-how_statisticians_do_it_.html

Mathematical Model

Finally, I finished reading one book: First Course In Mathematical Modeling by Frank  R. Giordano. This book took me almost a month to finish. Thank god. This book is quite useful and I have learned a lot of things because most of the things that I learned in degree level related to statistics and involved a linear function. But how to model something before collecting and after collecting your data? what if something is nonlinear? What needs to be to be taken into account?

I learned Survival Models, Loss Models, Applied Statistical Models, Stochastic Processes, Linear Models and many other models but most of the model involved more towards Statistics but this book more towards Mathematics without considering mean, variance and so on.

 

In Chapter 1, the author demonstrates a simple model and how it suppose to looks like.

In Chapter 2, what kind of processes involved to do modelling.

In Chapter 3, how to fit a model...using your data to fit a model or using your model to fit a data.

In Chapter 4, doing some experimental works to confirm your model.

In Chapter 5, using simulation to simulate your sample from population data.

And the rest of the chapters are more related to model certain situations and how to optimize your models.

Besides that, this book also shows some examples related how to model your situation related to physics, wars, economy, biology, interest rate, cooking (how long to roast your turkey? lol), drugs (pharmaceutical) and so on.

Honestly, this is kind of subject that should be teach during Form 6 or Degree level because most of the examples are using very simple secondary school maths and then relates it to applications rather than ask us to memorize all the formulas. 

Now is time to start my project and study for Final.
Final Exam Countdown: 20 days.


Night.

What people think about me...

Mathematics: Roast a turkey, need how long arh?

Okay, I confess that I never roast a turkey or eat a turkey before...but a chicken, yes!

It just so happens that when I'm was studying this book: First Course in Mathematical Modeling by Frank R. Giordano...I came across this interesting example.

This book in page 324 stated that

One of the general rule for roasting a turkey is the following: Set the oven to 400 ° F (204.44 °C) and allow 20 min per pound for cooking. 

1 pound = 0.4536 kg , 1 kg = 2.2462 pound

How good is this rule?

So, this book started with some assumptions, model the formula and testing the results.

Please be reminded that assumptions are not always hold, formula is not always true and the results are probably not always close to what we want but we are trying to approximate the results here...

Let:

t = cooking time for the turkey

*t certainly depend on the size of the turkey (all the turkeys certainly have different size) but we assume turkets are similar.

l = length of the turkey ( uncooked meat)

ΔT_m = the difference between the temperature of the raw meat and the oven

ΔT_c = the difference between the temperature of the cooked meat and the oven

k = coefficient of heat conduction for a particular uncooked food

Model:

t = f(ΔT_{m ,} ΔT_c, k, l)

So, after some extensively using some tricks we arrive at the formula

where t ∝ W^2/3

I'm not going to derive the whole formula here because I'm sure nobody going to bother about it. The W suddenly appear in the formula because we know W ∝ l³ . 

*The main reason is I'm lazy to type the whole thing out*

 

Just convince yourself the formula is like that. =)

 This formula t ∝ W^2/3 means the required cooking time is proportional to weight raised to the two-thirds power.

 Be patient with me, I almost done...

Take for an example:

If  
t₁ hours are required to a turkey weighing W₁ pounds and 
t₂ = is the time for a weight of W₂ pounds, 
then our formula become...

 

Let's consider we finally cooking a  real 10 kg turkey vs a real 3 kg chicken. 

According to the our rule, the ratio of cooking time is given by

 

But, if we use our formula, after we substitute into it

So our rule tells us that it will take 3.33 times as long to cook a 10 kg turkey compare to cook a 3 kg chicken and our formula tells us it will only take 2.23.

Which one is correct?

I don't know. We certainly need to test our formula or our model to make sure it is correct. Testing the results part is in the book, please read if you want to know but I'm not really sure whether our book gives a correct from a real world data or not.

I just want to say...finally we have at least a formula for cooking a turkey!

Bird Poop

This afternoon when I was washing my car, I found that there are some bird poops on it. I was interested to know and eager to make use of some probability courses that I have learnt in my statistics class.

Let start with X denote the number of bird poop that dropped on my car. We know that X follows Poisson distribution with mean λ = 1 bird poop per week.

Poisson formula: 

 P(X=x) = λ^x (e^-λ) /x!  for x=0,1,2,3...

Question:

1. What is the probability that I will get at least 8 bird poops on my car this week?

P(X ≥8) = 1- [P(X=0)+P(X=1)+ ...P(X=7)] = 0.000010249

Probability that I will get at least 8 bird poops on my car this week is around 0.000010249!

2.What is the probability that I will get exactly 8 bird poops on my car this week?

P(X=8) = 1^8 (e^-1) / 8! = 0.000009124.

Probability that I will get exactly 8 bird poops on my car this week is around 0.000009124!

Conclusion:

The probability of getting 8 bird poops or at least 8 is so low but I still get it. Dafuq stupid birds!

FU birds, I will panggang you next time if you ever poop on my car again!