stuck on this question

I don't understand the answer to
question 8 image-ebebf666-589b-45af-8e8c-72fe7a48ed5e8343634827695140289-compressed.jpg.jpeg

Reply 1

tonyiptony

Let's maybe go like this, instead of trying to interpret the marking scheme...

Let's ignore part (a) for now. Do you know how to do parts (b) and (c)? Can you at least write a line or two?
Sometimes that line is simply writing down a formula or something. That would be useful.

(edited 1 year ago)

Reply 2

alithealien

Ive done parts b and c, but I don't understand why the answer to part a is p= 1-a and p=1+a

Reply 3

mqb2766

The description in the solution/mark scheme is pretty much it. If you dont understand it then in detail
* Draw the data as two bars, one of height 8 centered on 1 and one of height 2 centered on 1+/-a (say a=1 so 0,2) for each of the two cases. Obviously one is a reflection of the other in x=1.
* Sketch the mean(s) one there. For a=1, the mean(s) would occur at 0.8, 1.2 (easy to calc?). The values are not that important, but theyd be weighted closer to x=1 because more of the data is there and they are a reflection of each other in x=1 (which is important)
* The variance or std dev is the (root) average squared deviation from the mean. Thinking about where the data and the means are, hopefully youd see that the deviation of each data points from 0.8 and 1.2 was 8 lots of +/-0.2 and 2 lots of +/-0.8. Squaring means you have an identical (root) average squared deviation so the std devs are the same when p is 1+/-a.

If youve done coding, then if one data set is p=1+a, the other is obtained from that one by -x+2, so a scaling of -1 (reflection about 0) and a shift of 2 (overall reflection about x=1). The +2 does not affect the std dev, neither does a gain of -1. So both std devs are the same when p=1+/-a.