# Caz c

### Finding the Variance of a coin toss, without using binomial method?

Set-up is a coin toss starting at x0. If heads, move to x1, if tails move to x-1. After n tosses, the coin should be on x0.

From the equation x_n = x_n-1 + F where F = +/- 1 , find the Var(x).

I think you have to square both sides leaving you:

(x_n)^2 = (x_n-1)^2 + 2Fx_n-1 + 1

Then take average values from both?

<x_n>^2 = <x_n-1>^2 + 2F<x_n-1> + 1

But from here I have no idea where to go, please help me step-by-step.

The variance can be calculated from binomial method to be n/4. So, I know that's the answer I need to get, but I'm not sure how to get there.

1 AnswerMathematics9 years ago### How do you solve an equation in the form: y = root(a) + root(a+ky) for y as a function of a and k?

In the form y = ....

Method step-by-step please

Mathematics9 years ago### Would you trust an eBay seller who was selling a Jailbroken and Unlocked iPhone 3GS?

I want to sell my iPhone 3GS 16GB online. At the moment I use it unlocked and jailbroken and I could effortlessly do it again if I restored my phone and wiped all the data off.

But I was wondering, I still have all the original boxing and cables and headphones, so is it more appealing to have a factory restored iPhone in its original box, nice and finished, OR to have one with all that but jailbroken and unlocked too. I realise I could sell it for more if its unlocked, but I think it would put a lot of people off buying it. What do you think?

4 AnswersMobile Phones & Plans9 years ago### What is the derivation of the dot product (Scalar product) of vectors?

Ive seen lots of variations on the explanation so I'd like one that explains both equations of the dot product. (One equation being the algebraic equation a_1b_1 + a_2b_2 + a_3b_3 ... etc)(The other equation being the geometric one =mod(a)mod(b)cos(theta) )

I've seen one explanation where the dot product is just DEFINED as being the sum of a_ib_i starting when i=0 and summing up to i=n where n is the number of dimensions of the vector. The geometric equation is quite easy to derive from this definition. However, I'd like the reason as to why the dot product is this algebraic equation.

Another explanation, described the algebraic equation FROM the geometric equation, saying that as two dimensions are parallel they're cosine is 0, and so you only pay attention to a_ib_i as opposed to a_i multiplying the entire other vector's dimensions.

Both these derivations only derive one equation of the two and both contradict, so id like a derivation of both equations for the dot product. Thanks!

2 AnswersMathematics9 years ago### Interest rate and debt question. How do you solve this equation for the value of n?

0 = 16.(26/25)^(n-1) + 25 - 25.(26/25)^(n)

How do you solve for an exact value of 'n'

The question in full was one on interest rates and paying off debt, but as I'm certain this general formula finds the answer, all I need is how to solve it. I'm familiar with numerical methods (Like Newton-Raphson) but I'm wondering how to find an exact answer for this?

Thanks

1 AnswerMathematics9 years ago### I've recently found that I talk to myself sometimes. Does this mean I'm somewhere on the autism spectrum?

When I'm on my own I found myself thinking about conversations I might have had or ones that I could have in the future. But sometimes I realise that my half of the conversation I am saying aloud or am imitating the body language and facial expressions I'd have as I was in the conversation. This happens quite often now, and has been since at least 6 months ago. I've seen children with autism doing the same, not realising theyre talking to themselves as they pace up and down. Could this be a sign that I am slightly autistic or is it too vague a symptom to pinpoint to anything. For all I know, it could just be me feeling subliminally lonely, or something.

2 AnswersMental Health9 years ago### What's the best way to make a 500 page printed document into a book?

Any tips on how to go about doing it. I think splitting it onto 2 pages per A4 and stapling down the middle won't suffice with so many pages in the book. Any ideas on how I could do this the best?

1 AnswerBooks & Authors9 years ago### Would a US electrical appliance draw more current from a household in the UK?

I have a 120V 0.33A ampliance designed for US mains.

If it is plugged into UK mains ~240V will it draw 0.33A the same, or will it draw 0.16A as the ampliance has a fixed amount of Power it will draw?

Either way I plugged it in and the 5A fuse protecting the plug of the appliance blew. Why would it draw MORE current from a UK mains?

1 AnswerPhysics9 years ago### What does the function f(x) = e^(ix) look like?

Can it be roughly estimated on cartesian coordinates, it might look similar to a sin curve as both y = sin(x) and f(x), second order differentiated equal the negative of the original function.

Is there a way to even represent it on an Argand Diagram?

2 AnswersMathematics9 years ago### I play a game where I flick a coin, if heads I move my counter forward by 1, if tails back by 1?

I start at 0, on average I will end up on 0 after n throws. <x_n> = 0

This isn't certain, so the frequency distribution follows a Normal Distribution Curve.

If after n throws, my position is x_n.

Then x_n = x_n-1 + k Where k = ±1

<x_n^2> = 2k<x_n-1> + k^2 + <x_n-1>^2

The Variance = <x_n^2> - <xn>

Variance = <x_n^2>

Using any of this information prove the Variance = n

Any help would be great!

1 AnswerMathematics9 years ago### Oxford Test - Probability Question?

The numbers shown by two dice are labelled d1 and d2; a score is constructed from these by the expression:

S = Ad1 + Bd2 + C, where A, B and C are constants.

Determine the values of A, B and C such that the range of possible values for S covers all integers from 0 to 35, with an equal probability of each score.

No calculators allowed in test, and please show all your working/thoughts in your answer. Thanks :)

1 AnswerMathematics9 years ago### Physics Geometry Question (Oxford Physics Aptitude Test Question)?

An astronaut arrives on the planet Oceania and climbs to the top of a cliff overlooking the sea. The astronaut's eye is 100 m above the sea level and he observes that the horizon in all directions appears to be at angle of 5 mrad below the local horizontal.

What is the radius of the planet Oceania at sea level? [4]

How far away is the horizon from the astronaut? [3]

[Hint: the line of sight from the astronaut to the horizon is tangential to surface of the planet at sea level.]

Additional info: You're not allowed any calculators or tables in the test, so I'm not entirely sure how you do this one without a calculator for the difficult calculations. I think it may have something to do with sin(θ) ≈ θ when θ<<<1

1 AnswerPhysics9 years ago### Find an equation for the total impulse applied holding a beaker still as it fills up with water?

Where t is time

dV/dt from tap = k

Density of water = P

Acceleration of gravity = g

I got two answers for this one:

One answer I got: I = 1/2k*P*g*t^2

But I also got: integral (k*P*g) dt

Which would only give: I = k*P*g*t

I think the first answer I found is right, so could somebody show me how to do it the latter way so I can see where I've gone wrong, thanks.

1 AnswerPhysics9 years ago### Prove that Re( z / z+w ) = 1/2?

If z = a + bi

w = b + ai

Re(x) is the real part of the complex number

Where i is the squareroot of -1

Please show all working out

3 AnswersMathematics9 years ago### Would 'innocent until proven guilty' still apply if builders stole your television, whilst you were out/?

So, imagine I had builders coming around to install double-glazing or something (I don't know?) and you had to leave them in your house alone, as you had a busy schedule. When you come home, your wall-mounted tv is gone with the wall bracket broken. Builders say that the wall bracket broke of its own accord, and the tv smashed, so they placed the broken tv into the skip outside with all their waste too. The skip was taken away when they were finished (Which happened to be before you came home) and they cleared up the bits of tv as they cleared up after themselves.

Are they innocent until proven guilty? Because they really could have just broken it off its wall mount and stolen it!

6 AnswersLaw & Ethics9 years ago### How do you solve: (1+x)^(-1/2) = e^(-x)?

I've done Core Maths A-Level, but I don't think I can solve this using the knowledge I know.

1 AnswerHomework Help9 years ago### Does the weight of fluid displaced equal the weight of the object OR does the volumes of both equal?

Archimedes principle says:

Weight of fluid displaced = weight of object submerged (http://en.wikipedia.org/wiki/Archimedes'_principle...

BUT 'fluid dynamics' says Volume of fluid displaced = Volume of object submerged

http://en.wikipedia.org/wiki/Displacement_(fluid)

Is the second article only valid for water, and it just hasn't correctly stated that? Because how can it be true for every fluid?

1 AnswerPhysics9 years ago### What does the ionic lattice of MgCl2 look like?

Everyone is comfortable with the simple lattice on NaCl, whereby its just like a chessboard, one Na+ then one Cl- with no two similar ions touching. But what does a lattice on MgCl2 look like? Where there's two Cl- ions for every Mg2+ ion.

1 AnswerChemistry9 years ago### How do I keep a gas escaping from holes in a pipe to the same rate as each other?

Basically I have a long metal pipe, which has lots of tiny drilled into it all the way along, where a gas will escape from. But what way of feeding the gas into the pipe will ensure that the gas escapes by the same amount at every hole down the entire length of this pipe?

1 AnswerDo It Yourself (DIY)9 years ago