Safety Car Deployed

Mathsy stuff that I will need later

5)1) on probability:

first assume that y>=x, then you can draw a graph showing that, for a random pdf, if y>=x then the area under the graph from -infinity to x is less than for -infinity to y

F(y)=integral(-infinity, y) f(y)dy, which equals integral(-infinity,x)f(y)dy + integral(x,y) f(y)dy
so for F(y) to be greater than or equal to F(x), we must have that integral(-infinity,y)f(y)dy must be greater than or equal to integral(-infinity,x)f(y)dy.

this implies that integral(-infiinity, y)f(y)dy - integral(-infinity,x)f(y)dy >= 0

this means that integral(x,y)f(y)dy must be positive

as f(y)>=0 for all y in M
this must be true by definitiion of pdf

so as integral(-infiinity, y)f(y)dy - integral(-infinity,x)f(y)dy = integral (y,x) f(y)dy, which must be >=0
this is true.
5)2)
we know from def of pdf that the total area under a pdf=1. 
as x tends to -infinity, F(x) tends to integral(-infinity,-infinity)f(y)dy 
which tends to 0 as, by definitiion of the integral, the integral(a,a)f(x)dx must be 0. 
we can also show this by integrating , integral(-infinity,-infinity)f(y)dy= integral f(-infinity)dy-integral(-infinty)dy which is obviously 0

as x tends to infinity, then F(x) tends to integral(-infinity, infinity) f(y)dy which by definition is one, as this integral covers all the area under the pdf.

the probabilistic meaning of this is that 0<= P(X<=x)<=1 so a probability must be between 0 and 1 and the total area under a pdf is 1.

For my own personal use…

I’ve lived a lot of different lives
Been different people many times
I live my life in bitterness
And fill my heart with emptiness

And now I see, I see it for the first time,
There is no crime in being kind
Not everyone is out to screw you over.
Maybe, oh just maybe they just wanna get to know ya.

Now the time is here,
Baby you don’t have to live your life in fear
And the sky is clear, is clear of fear

Don’t wanna live in fear and loathing
I wanna feel like I am floating
Instead of constantly exploding
In fear and loathing

Got different people inside my head
I wonder which one that they like best
I’m done with tryin’ to have it all
And endin’ up with not much at all.

And now the time is here,
Baby you don’t have to live your life in fear
And the sky is clear, is clear of fear
Of fear

Don’t wanna live in fear and loathing
I wanna feel like I am floating
Instead of constantly exploding
In fear and loathing.

And when the time comes along
And the lights run out,
I know where I will belong
When they blow me out.

Don’t wanna live in fear and loathing
I wanna feel like I am floating
Instead of constantly exploding
In fear and loathing.

I wanna be completely weightless
I wanna touch the edge of greatness
Don’t wanna be completely faithless
Completely faithless.

When the time comes around
When the lights will go out
When the time comes around
When the lights they go out

Got another year of my life planned out…

So, after this three-year degree is finally done, they’ll be one more year at Uni…

Now, I wanted to do the 4th year at Loughborough, like the other three, simply because I like it there so much, but alas, Leicester is a much better option…

So I’m going for a PGCE in Secondary Education. Loughborough will charge me £9,000 in tuition fees and give me a Masters in return.

Leicester will charge me £9,000 in tuition fees, give me a Masters in return and either £20,000, £15,000 or £12,000 if I get a First, 2.1 or 2.2 in my current three year Maths degree, so y’know, Leicester have a nice financial incentive.

The joys of there being a lack of Maths teachers in the country :)

In other news, if you decide to be a primary school teacher, you’ll only get between 5 and 10 grand, and if you teach Social Sciences at secondary school, you get nothing…

Anyways… two more years of ordinary Uni to go yet :)

I wanna’ feel like I am floating, instead of constantly exploding

There is no crime in being kind

Life

I rarely blog nowadays, but here goes.

I don’t live with either of my biological parents. I don’t know my real Dad and my Mum left. My biological Dad is running around unknown probably with his own life, but I have no interest in corrupting my life with him just yet. It feels as if Mum wants barely anything to do with us anymore, and is simply in contact with us just for the child tax credit she gets. Alas, not from me, hence the less contact with me.

Dad can’t really afford much, and with Mum thinking she can fall back on her husband she seperated from for money whilst she goes travelling to Lincoln every weekend to meet some man she calls her new ‘boyfriend’ who dumps her within a fortnight, money is crap.

I’m at the stalling point of life it seems. I’m in love, and hve so many dreams and desires to fill, yet I’m stuck at home and University, simply waiting for the 4 years to go by so I can finally start what I believe to be life.

I mean, I want to leave home. I want to get my own place. I want to have a bookshelf with our books. I want to have our walls filled with silly pictures of us. I want to eat our food together when we want. I want to be able to come back at night and just collapse on our bed.

I feel as if I’m wasting time at Uni. I mean, I want this degree, and I know it’s worth it, but it feels it’s just another 4 years of stalling life. If I just got a job, surely I could’ve made my dreams come true faster? Ahh, I complain now, but it’ll be worth it. Hopefully.

I just want to grow up. I just want to live my life and rely on nobody. I can’t wait to get to live in a place I can call my own home, with the woman I love.

Just a small little flat will do. Need to win the lottery, obviously.

Next weekend we get to live a little. It’ll be good. I’m looking forward to living.

I rarely blog nowadays, and I probably won’t for a little bit longer.