Math Is Fun Forum

lindah

Member

Registered: 2010-01-25

Posts: 121

PDF to CDF

http://imageshack.us/photo/my-images/3/19637915.png/

Hi guys,

My last question before crunch time, if you guys may. This one is a bit long (sorry)

a)  I have found k = 6/13 after using the property that a density function should equal 1

b)   In finding the CDF, I integrate each term in the piecewise function and solved for the constant as follows:

I solved for them and for A= 9/13 and B = 9/13. Is this correct?

For the CDF I'll obtain
0 for x<-1

for -1<x<0

fpr 0<x<1
0 for x>1

c)   In trying to obtain the mean I integrate

But I am obtaining a negative mean?

d) I can complete this myself if I get the mean correct

e) To find the probability X>0 Ive used

Last edited by lindah (2011-06-08 09:00:15)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: PDF to CDF

Hi lindah;

a) k = 6 / 13 is correct.

b)Should be

for -1<x<=0 not -1<x<0

Same thing for the next one. Should be 0<x<=1 not 0<x<1

This is kind of tricky 0 for x>1. Are you sure about that?

c )I do not think that the mean of f(x) is computed like that.

d) Waiting for the correct mean.

e) Looks good.

---

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.

lindah

Member

Registered: 2010-01-25

Posts: 121

Re: PDF to CDF

Argh! So far I've only seen cdf-> pdf questions in my course

I'm not sure about the 0 for x>1 for the cdf, do you have any hints? Edit: Should this be 1, since a cdf ranges from 0 to 1?

c) I haven't dealt with a piecewise version before - can you give me a hint how I would set this up?

Last edited by lindah (2011-06-08 12:08:28)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: PDF to CDF

Hi;

The way I understand CDF it means the probability up to here. So I would say it might be a 1. Because when you say what is the probability from - infinity to 10 , it would be a 1.

For c)

You are calculating the expected value, I thought the average value of a function is computed using this formula.

Using that the average value is 1 / 2.

---

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.

lindah

Member

Registered: 2010-01-25

Posts: 121

Re: PDF to CDF

Hi bobbym,
Isn't that simply the integral of the function?

I'm working of this:
http://en.wikipedia.org/wiki/Expected_v … m_variable

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: PDF to CDF

Yes, the question says the mean of f(x). Not the expected value.

---

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: PDF to CDF

Hi bobbym,

I guess lindah has done correctly.
The question is to find mean and s.d of X.
http://www.zweigmedia.com/RealWorld/cprob/cprob3.html
And average is

How do we calculate the average of a function when domain is (-∞,∞) ?

Last edited by gAr (2011-06-08 16:07:22)

---

"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: PDF to CDF

Hi gAr;

How do we calculate the average of a function when domain is (-∞,∞) ?

I have a couple of questions about this. Is the expected value the same as the mean in this case?

Actually the function really only has a value other than 0 between [-1,1]. So I took a = -1 and b = 1. That is how I got 1 / 2.

I tried an experiment of choosing lots of random reals between -1 and 1 for x. When I plugged them into the piecwise function that is her f(x) and added them up I got a mean of 1 / 2.

---

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: PDF to CDF

Hi bobbym,

Looking at some other sources, I guess it may be the expected value which is required here.
But I feel strange since we get a negative value.

My question on average was a different one, unrelated to this. Sorry for not mentioning before.

---

"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: PDF to CDF

I do not see how you can use that formula for domain of - infinity to plus infinity either.

If you plot the piecewise function it looks like the mean is positive.

---

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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: PDF to CDF

hi Lindah,

I see from another post that your exam is today.  Good luck! 

I've only just picked up on this thread.  In case you read this before the exam I'll throw in my contribution.

a and b and e correct by my reckoning.

The CDF has to be continuous at x = 0 (unlike the pdf which isn't).  It makes no differnece whether you put < or ≤ because a probability at a single value is meaningless for a pdf.

is correct.  Look at the graph of the pdf.  There's lots more area to the left of zero than to the right so a negative expected value is fine.  (at the moment I don't get your negative value but I've probably made an arithmetical error)  EDIT: checked my working three times.  I keep getting E[x] = -1/13

mean and expected value are the same thing for a pdf.

after x = 1 the CDF = 1 for all x.

Bob

Last edited by Bob (2011-06-08 21:04:20)

---

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

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: PDF to CDF

Hi bobbym,

Okay.
I'll read some more about it.

Hi Bob,

Thanks for clarifying.

---

"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: 10,621

Re: PDF to CDF

good morning bobbym

I do not see how you can use that formula for domain of - infinity to plus infinity either.

For this pdf the CDF is zero below -1 and one above +1

For a pdf that has non zero values for all x such as the normal distribution the pdf values tend to zero as x goes to + or - infinity.

So the expected value works out ok even then.

My graph is a trapezium for x less than zero and an inverted parabola between 0 and 1.  The left hand side 'looks' a lot more area than the right hand side.  So it's more likely that x is negative => a negative expected value is 'expected' whoops sorry for the pun.

Bob

Last edited by Bob (2011-06-08 21:16:46)

---

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

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: PDF to CDF

Hi Bob,

Good morning!

---

"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: 10,621

Re: PDF to CDF

good morniong gAr

Thanks.  Just spotted my error.  put 1/2 instead of 1/4.  I blame it on senility! 

I've added a 'sketch' of the graph to my previous post.

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

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: PDF to CDF

Hi Bob,

Okay. I have done such mistakes many times, so it's obviously not senility!
Thanks for the graph.

---

"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: PDF to CDF

Hello gAr and bob bundy;

In my case it is obviously senility. Perhaps a high concentration of heavy metals is interfering with normal synaptic action.

Now about your graph, I am on the floor laying on my back with the laptop perched on my chest. From that angle the right side looks bigger. When I am again sitting like a human being I am sure I will see it your way. Till then I will take your word for it.

---

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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: PDF to CDF

and I thought Joda could see all things with the force alone.

Perhaps you should lay off the heavy metals for a while.

Or maybe you should analyse the key word 'lap   -  top'  ?

Bob

Last edited by Bob (2011-06-08 21:55:44)

---

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: PDF to CDF

Yes, I will lay off the heavy metals, I will miss the lead though.

As soon as my spine returns I will be sitting.

---

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: PDF to CDF

Hi bobbym,

Yes, stay away from heavy metal music when doing maths!

May your spine get well soon.

---

"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: PDF to CDF

Hi gAr;

Not music, actual heavy metals, like lead, cadmium, mercury, antimony etc. Impurities present in our water, food and air.

It is just my back acting up, I was going to go play pool this morning but that is not going to happen.

---

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: PDF to CDF

Hi bobbym,

This time, I was trying to be funny!
Anyway, are the heavy metals really there, in high concentrations?
I think it's better to stay away from pool, it may worsen your back problem.

---

"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: PDF to CDF

I missed that. That is funny.

I have to stay away from it. I am reduced to doing only 2 things. Math and eating.

---

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: PDF to CDF

Okay.
Enjoy the math, and food.

---

"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: PDF to CDF

I am solving a nice problem right now. I just have to clean it up.

---

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.