Math Is Fun Forum

suhana

Member

Registered: 2011-02-25

Posts: 31

help me again..please about cumulative distribution function

:faintthis question about cumulative distribution function..

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: help me again..please about cumulative distribution function

Hi,

I believe there is a mistake in the question.
f(x) is 3 in the region (2,3]. Probability must not be greater than 1, obviously.

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: help me again..please about cumulative distribution function

Hi;

We would make c = - .8 to make this a valid probability mass function. In the sense that over the region 0 to 3 the area would equal 1.

But I do not like it either. In order  for a function to be a PDF it must satisfy two conditions.

The area must equal 1 and f(x) >= 0 for all real x.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: help me again..please about cumulative distribution function

The definition requires that f(x) ≥ 0, isn't it?

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: help me again..please about cumulative distribution function

Yes, see my post above you we were posting at the same time.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: help me again..please about cumulative distribution function

Yes, we posted at the same time.
May be it should be 0.3 instead of 3.

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Bob

Administrator

Registered: 2010-06-20

Posts: 10,649

Re: help me again..please about cumulative distribution function

hi bobbym and gAr,

I agree there's an error here.

Suppose it is meant to be 0.3 rather than 3.  Then it makes better sense.

see diagram

Bob

edit You just got that suggestion in before me.

Let's go with that idea.  After all it's the method that suhana needs to understand.

I'm in the middle of the probability question so I'll leave this one to you guys.

Last edited by Bob (2011-02-26 03:14:01)

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: help me again..please about cumulative distribution function

As it stands it is not a PDF. The value of c = -.8 makes f(.1) = -.82

That is impossible. Something is not right.

How can the constraint  2 < x <= .3 exist?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

suhana

Member

Registered: 2011-02-25

Posts: 31

Re: help me again..please about cumulative distribution function

wuaaa :touched...i dont know about all questaion because my lecutrer give this assingment and last date 2/3/2011

my couse data com and networking,i dont know why we must to learn about statistics...stress because almost a 1 week i try to understand and do it my own..but still no solution..

sorry all you trouble..

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: help me again..please about cumulative distribution function

Everyone should learn about statistics. People walk around every day making incorrect decisions because they know no statistics. Someone on another thread is going to insist that because a red card comes up and then a black one that you should pick a red now because he thinks that it should be red next.

It is no trouble to work on your questions. Welcome to the forum.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

suhana

Member

Registered: 2011-02-25

Posts: 31

Re: help me again..please about cumulative distribution function

As it stands it is not a PDF.?
chance to file pdf?or what?
my question have a problem or wrong question?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: help me again..please about cumulative distribution function

As I understand it I do not think it is a PDF. There could be a typo.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

suhana

Member

Registered: 2011-02-25

Posts: 31

Re: help me again..please about cumulative distribution function

PDF= did you main prbability distribution function?

I have taip wrong title, which actually is about probability density function of continuous random variable

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: help me again..please about cumulative distribution function

I think they are both the same. The typo could be on the 3.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

suhana

Member

Registered: 2011-02-25

Posts: 31

Re: help me again..please about cumulative distribution function

c-0.2x<--chance 3?

or

0=<x=<2 chance 3?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: help me again..please about cumulative distribution function

Hi;

Please do not worry about this one. I think the question is not correct.

What was the last thing in statistics that you understood and are comfortable with maybe we can go from there.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

suhana

Member

Registered: 2011-02-25

Posts: 31

Re: help me again..please about cumulative distribution function

owh okey tq..

Bob

Administrator

Registered: 2010-06-20

Posts: 10,649

Re: help me again..please about cumulative distribution function

hi suhana,

The problem with this question is the '3' in the definition of the pdf.

If the function is 3 for 2 < x < 3 then the area of this rectangle on the graph is 3 x 1 and that's too much for a pdf.

The total area under a pdf graph MUST be 1.  It's built into the definition of all pdfs.

gAr and I think that maybe there's a printing error and it should be 0.3

The question makes sense then and can be done.

I've modified the question and posted it below along with the correct graph.

So, what are the answers?

(a)  f(x) = c - 0.2x between 0 and 2.

f(0) = c
f(2) = c - 0.4

So the total area under this graph ( trapezium and rectangle) is

A = (c + c - 0.4)x2/2 + 0.3 x 1

This must be 1 (by definition) so you can solve for c.

I made it c = 0.55

(b) E(x) is the 'expected value' and is found by multiplying 'x' by F(x) and summing for all values of x

In practice you only need to sum between 0 and 3 because f(x) is zero elsewhere.

I made this 1.31666....

(c) 

(d)  The Cumulative function is the 'area under the graph' function, ie

For the first part

when 0 < x < 2.

At x = 2

Between 2 and 3 I haven't bothered to use an integral as it's just the area of a rectangle

Note:  when x = 2            F(x)= 0.7 so it is continuous with the other F

and at x = 3             F(x) = 0.7 + 0.3 = 1 which is required for a cumulative function.

Hope that helps, 

Bob

Last edited by Bob (2011-02-26 07:59:41)

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

suhana

Member

Registered: 2011-02-25

Posts: 31

Re: help me again..please about cumulative distribution function

thank's  bob .. but i ask you back after my friends wedding ceremony

see you leter...

Bob

Administrator

Registered: 2010-06-20

Posts: 10,649

Re: help me again..please about cumulative distribution function

ok,

Have a great wedding party!

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

suhana

Member

Registered: 2011-02-25

Posts: 31

Re: help me again..please about cumulative distribution function

(a)  f(x) = c - 0.2x between 0 and 2.

f(0) = c
f(2) = c - 0.4

So the total area under this graph ( trapezium and rectangle) is

A = (c + c - 0.4)x2/2 + 0.3 x 1

This must be 1 (by definition) so you can solve for c.

I made it c = 0.55 <--my calculate--> (0+0-0.4)x2/2 + 0.3 x 1 =-0.1?how can the number of 0.55..?

the next question
how tu calculate from calculator  casio?you have website or address to learn about this?

suhana

Member

Registered: 2011-02-25

Posts: 31

Re: help me again..please about cumulative distribution function

opss not out ..

That finish after 2pm weading i continue to do this question ..

emm.how to use infinity from calculator..
do you have any web or you tube because right now not see from my search

suhana

Member

Registered: 2011-02-25

Posts: 31

Re: help me again..please about cumulative distribution function

aii...bob
can u explain answer u give me..
becau that are defrean totally from me..

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: help me again..please about cumulative distribution function

Hi;

A = (c + c - 0.4)x2/2 + 0.3 x 1

Is this what you are having problems with?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

suhana

Member

Registered: 2011-02-25

Posts: 31

Re: help me again..please about cumulative distribution function

yup...because i have answer -0.1,why?