Competition - post a photo you've taken of nature >>

Stats question

Hi there, wondered if anyone had any clue at all re: the attached question. I'd be super-grateful for any tips.

I think it starts off just about OK:

I assume that the answer to a) is b, though one or both of the sketch you get & my scan is so bad that it's hard to say.

And then the answer to b) must be 1, right, you know that without looking at the graph.

But then on c)... I suppose I thought that the total area under the line must equal 1 (right?), so I split that area up into two areas, namely:

a rectangle, height a, width 1(?), area a
a right angle triangle, width a, height (b-a) = (3a-a) = 2a, so area = a

so the area under the line equals 2a... so a must equal 1/2... but then that leaves b = 3/2, which feels rather unlikely...

am I just totally not getting this or something??

thanks in advance.

mathimg.jpg142.7KB

Reply 1

ghostwalker

Original post by puffyisgood

I assume that the answer to a) is b, though one or both of the sketch you get & my scan is so bad that it's hard to say.

'Fraid not.

With a continuous random variable, what's the probabilty that it can equal a specific value?

And then the answer to b) must be 1, right, you know that without looking at the graph.

Yes.

But then on c)... I suppose I thought that the total area under the line must equal 1 (right?), so I split that area up into two areas, namely:

a rectangle, height a, width 1(?), area a
a right angle triangle, width a, height (b-a) = (3a-a) = 2a, so area = a

so the area under the line equals 2a... so a must equal 1/2... but then that leaves b = 3/2, which feels rather unlikely...

Looks fine. It's the answer to part a) that's throwing you i suspect.

Reply 2

RDKGames

Study Forum Helper

Original post by puffyisgood

...

To add onto what ghostwalker said, note that for a continuous random variable, you have

\displaystyle \mathbb{P}(X=\alpha)=\mathbb{P}(\alpha \leq X \leq \alpha)

which by definition is equivalent to

\displaystyle \int_{\alpha}^{\alpha} f(x) .dx

Reply 3

puffyisgood

Original post by ghostwalker

'Fraid not.

With a continuous random variable, what's the probabilty that it can equal a specific value?...

ha, ok, i'm trying to do the questions without having read the notes.

i suppose the probability it equals a specific value is... next to nothing, zero a decent approximation? yes, that must be right since there are infinitely many specific [non integer] numbers between 0 and 1??

Reply 4

ghostwalker

Original post by puffyisgood

It's not next to nothing, it is zero - see RDKGames' post above.

Reply 5

puffyisgood

Original post by ghostwalker

It's not next to nothing, it is zero - see RDKGames' post above.

thanks, though said post scared me a little, we've not done any calculus yet, so I avoided.

anyway, would i be right in assuming that the following is an OK decent answer to (d) [apologies that a bit blurry, my phone camera is quite cheap/scratched]?

IMG_20171127_164034183.jpg540.4KB

Reply 6

RDKGames

Study Forum Helper

Original post by puffyisgood

thanks, though said post scared me a little, we've not done any calculus yet, so I avoided.

If you were to draw

X=1

then all you'd see on the graph is a straight vertical line going up from the bottom to the shown line in the picture. What is the area of the line? Well the line does't even define an acceptable a 2D region, but it can be thought as being a 2D region with base length 0 and height being whatever. So in essence, the area of this 2D region would be 0 since anything multiplied by 0 is 0.

Reply 7

RDKGames

Study Forum Helper

Original post by puffyisgood

anyway, would i be right in assuming that the following is an OK decent answer to (d) [apologies that a bit blurry, my phone camera is quite cheap/scratched]?

You need to explicitly show that the trapezium on the right has bigger area that the trapezium on the left, and I'm pretty sure they would go all the way down to the X axis.

Reply 8

puffyisgood

Original post by RDKGames

You need to explicitly show that the trapezium on the right has bigger area that the trapezium on the left, and I'm pretty sure they would go all the way down to the X axis.