Math Is Fun Forum

ConfusedWithStats

Guest

A Stats Equation

Hello, I have done a lot of working out and ended up with this equation:

Which is the same as

But I don't know how to re-arrange this to get the answer, could you show me a step by step way of solving this? I'm not sure how to get the variable x on one side.

Thank you in advance.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: A Stats Equation

Hi ConfusedWithStats;

You can solve for x by iterative methods, interval bisection, newtons iteration... Or you can get the taylor series of the LHS and truncate to a quadratic like this.

1 - x^2 / 2 = .8 and solve this quadratic or you can truncate to a cubic 1 - x^2 / 2 + x^3 / 3 = .8. The question is how accurate do you want the solution to be?

x = -0.528328090256478241250183444471068676140007421443980539853264...
x = .82438830903298460937957300776559646539962691434072...

Last edited by bobbym (2009-09-30 17:32:22)

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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.

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: A Stats Equation

Wow this makes me realise how much I love my graphics calculator... just nSolve( and out pops the answer.
Iteration... Taylor series? eww

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: A Stats Equation

Hi identity;

Agreed! But those methods are the reasons why there is a graphical calculator.

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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.