Hey there,
I was wondering if anyone could shed any light on thse questions. My knowledge in this area is sketchy. I would welcome any help greatly!
Kind Regards,
Ross
I have time for Q19 (i) and (ii):
Mean: $\displaystyle E(X) = \int_{-\infty}^{\infty} x \, f(x) \, dx = \int_0^1 x \, 2 (1 - x) \, dx = \int_0^1 2x (1 - x) \, dx = \, ....$
Variance: $\displaystyle Var(X) = E(X^2) - [E(X)]^2$.
$\displaystyle E(X^2) = \int_{-\infty}^{\infty} x^2 \, f(x) \, dx = \int_0^1 x^2 \, 2 (1 - x) \, dx = \int_0^1 2x^2 (1 - x) \, dx = \, ....$
(iii) You should do some research.
For Q20, read this: http://en.wikipedia.org/wiki/Standard_error_(statistics)
Regarding (iii):
1. Read this (well I think it's funny and it's something I didn't know): Urban Dictionary: grauniad
2. Read this regarding iii (c): Poisson distribution
3. Read this regarding iii (a): Poisson process - Wikipedia, the free encyclopedia
Now read this: Poisson distribution - Wikipedia, the free encyclopedia
So which option does that leave ....?