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Pg 280 Calculating X (p(x<=x)) Calculations Coming out incorrect

#1 User is offline   AShiraz 

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Posted 11 August 2009 - 04:36 PM

I am looking at the column on the right for x P(X<=x).

I see when x = 2

P(X<=x) = 1 - q^r
P(X<=2)= 1-(0.8)^2
P(X<=2)= 1- 0.64
P(X<=2)= 0.36

xP(X<=x)
2* 0.36 = 0.72
This is my value which is different from the one in the book.
The value in the table is 0.52.

Why is that?

I dont see this in the errata so I am assuming there is something wrong.

This post has been edited by AShiraz: 11 August 2009 - 04:38 PM

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#2 User is offline   jr.larsen 

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Posted 11 August 2009 - 05:02 PM

The heading for the third column is misleading (or maybe just plain wrong!)

The third column is the sum of the values in the second column, up to that value of x. It is like a cumulative expectation.

0.2
0.2 + 0.32
0.2 + 0.32 + 0.384
...

A better heading might be:
Sum(from r = 1 to r = x) of xP(X = r)
but using sigma notation.

The book has another stab at the notation as the label to the vertical axis of the graph at the bottom of the page. There the sigma symbol is included, but I still think it's slightly odd notation.
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#3 User is offline   AShiraz 

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Posted 12 August 2009 - 08:53 AM

Bless you Sir! thank you for your response if the third column and the axis is :

Sum(from r = 1 to r = x) of xP(X = r)

Why is it saying :
Sum( xP(X <= r) )

?
There is the less than equal to symbol which is throwing me off. Lets include this in the errata?


QUOTE (jr.larsen @ Aug 11 2009, 05:02 PM) <{POST_SNAPBACK}>
The heading for the third column is misleading (or maybe just plain wrong!)

The third column is the sum of the values in the second column, up to that value of x. It is like a cumulative expectation.

0.2
0.2 + 0.32
0.2 + 0.32 + 0.384
...

A better heading might be:
Sum(from r = 1 to r = x) of xP(X = r)
but using sigma notation.

The book has another stab at the notation as the label to the vertical axis of the graph at the bottom of the page. There the sigma symbol is included, but I still think it's slightly odd notation.


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#4 User is offline   jr.larsen 

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Posted 12 August 2009 - 11:14 AM

Actually, it should be
Sum(from r = 1 to r = x) of rP(X = r).

The book says
Sum(xP(X <= x)),
at least on the axis it does.

The book seems to be using a shorthand to suggest adding the expectations for each value of X up to and including x. I've never seen that notation used before and I don't think it makes much sense.

Yes, it's probably worth flagging as errata, especially as the table doesn't even have the sigma symbol.
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#5 User is offline   AShiraz 

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Posted 12 August 2009 - 12:01 PM

It sort of makes sense to say P(X<=x) because that would be the area under the curve if I am not wrong. This would be evident to those who have taken a Prob Stats course but will not be to someone who is looking at it with fresh eyes.

QUOTE (jr.larsen @ Aug 11 2009, 05:02 PM) <{POST_SNAPBACK}>
The heading for the third column is misleading (or maybe just plain wrong!)

The third column is the sum of the values in the second column, up to that value of x. It is like a cumulative expectation.

0.2
0.2 + 0.32
0.2 + 0.32 + 0.384
...

A better heading might be:
Sum(from r = 1 to r = x) of xP(X = r)
but using sigma notation.

The book has another stab at the notation as the label to the vertical axis of the graph at the bottom of the page. There the sigma symbol is included, but I still think it's slightly odd notation.


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#6 User is offline   AShiraz 

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Posted 12 August 2009 - 05:17 PM

QUOTE (jr.larsen @ Aug 12 2009, 11:14 AM) <{POST_SNAPBACK}>
Yes, it's probably worth flagging as errata, especially as the table doesn't even have the sigma symbol.



So I will try to put this in to consideration for errata. I am so grateful that Kathy Sierra and Bert Bates started these books. Also thank you Ms. Griffiths for the stats book!
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#7 User is offline   jr.larsen 

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Posted 13 August 2009 - 12:39 AM

QUOTE (AShiraz)
It sort of makes sense to say P(X<=x) because that would be the area under the curve if I am not wrong.


That would be the area under the graph up to x, for a continuous distribution. However, the example is not looking for the area, or the straight probability. It's looking to keep a running total of the expectation.
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#8 User is offline   AShiraz 

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Posted 13 August 2009 - 05:08 AM

QUOTE (jr.larsen @ Aug 13 2009, 12:39 AM) <{POST_SNAPBACK}>
That would be the area under the graph up to x, for a continuous distribution. However, the example is not looking for the area, or the straight probability. It's looking to keep a running total of the expectation.


Ok then there is no excuse for that representation. It is all the more confusing since the page before it mentions that P(X<=r) = 1-q^r and I was busy plugging that in. I notice there is a small note saying this is the running total but that is a very confusing and conflicting message.

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