• Welcome to Maher's Digital World.

Maths & statistics exercises / French and English lessons

Started by scarface, June 16, 2013, 11:58 PM

Previous topic - Next topic

Daniil

Scarface you're a cool one. I'm recoginsing here a formulas we learnt at math statisitics at univercity. But I never can imagine that someone can play with this just for fun, like you do. :) We using this Poisson distribution in theory of digital signal processing and in calculation statistical distribution of marketing parameters.

scarface

#21
We have seen that Daniil, like humbert was eager to do some statistics. And no matter why, it can be useful in real life, not if your only hobby is to watch TV of course.
Now we are going to have some more difficult exercises. if shadow97 wonders why he has not done that at school, its normal, perhaps he will see that if he wants to become an administrator in a statistics institute.
So here is the exercise:
X is a random variable with the following density of probability:
f(x,c)=e^(-(x-c)) if x>c  (c is an unknown real parameter)
0 otherwise
1) calculate the expected value of X
2) deduce an estimator of c based on the random vector Xn={X1,...,Xn}
is it biased or convergent?
tips: we are going to use the expected value with the law of the great numbers.

scarface

#22
Here is a correction for the exercise.
For those who will work on that, its an opportunity because I explained the moments method used to obtain an estimator. In this case its simple though.


humbert

@Scarface - how far up in math did you go, and how long ago did you study it? Sadly I only went as far as Calculus I, which isn't a whole lot. Bad circumstances made it impossible for me to keep studying.  :(

scarface

#24
What I did is not your business humbert. But I can assure you I was good at statistics before doing these exercices. Im doing this to eventually take some exams and move on to other jobs.

Of course, We havent finished with the last exercice yet.
Here are 2 more questions:
3) Calculate the limited distribution of the estimator ( using the theorem of the central limit).
4) Calculate the bound of Cramer-Rao for the estimator (very difficult).


humbert

@Scarface â†' I don't understand why you're upset. All I asked was how far up in math did you go in school. Of course it's possible that you studied more of it as well as statistics on your own. Was that what happened, if you don't mind telling us?

scarface

I studied mathematics...10 years ago. I just regret not to have done something useful like Ahmad. So I wont talk about the past.  And dont think its easy, if I know how to resolve question 3) I have no idea how to do 4)

humbert

Quote from: scarface on January 30, 2014, 01:15 AM
I studied mathematics...10 years ago. I just regret not to have done something useful like Ahmad. So I wont talk about the past.  And dont think its easy, if I know how to resolve question 3) I have no idea how to do 4)

It's past midnight over there. Shouldn't you be asleep?  :)

I'm like you in that I too regret that I was not able to continue studying math, physics, stats etc. It's a long story. Like you said, the past is the past, we must continue forward. And yes, hopefully Ahmad will finish medical school and graduate as a doctor.

scarface

#28
yes it is. and I'm getting up at 7 am because I'm working but I'm not sleepy. Perhaps because I'm drinking a lot of coffee each day.

Shadow.97

Quote from: scarface on January 30, 2014, 01:27 AM
yes it is. and Im getting up at 7 am because Im working but Im not sleepy. Perhaps because Im drinking a lot of coffee each day.
-Offtopic-
I quite often stay up to 4-5AM on school days where I have to get up at 7. I really can't fall asleep at night. I go to school, and come home, sleep then do what I want for the rest of the hours.
Regarding coffee though. How much do you drink? I love coffee, strong coffee with a little milk.