Date | May 2021 | Marks available | 2 | Reference code | 21M.2.AHL.TZ2.6 |
Level | Additional Higher Level | Paper | Paper 2 | Time zone | Time zone 2 |
Command term | Show that | Question number | 6 | Adapted from | N/A |
Question
A continuous random variable X has the probability density function fn given by
fn(x)={(n+1)xn, 0, 0≤x≤1otherwise
where n∈ℝ, n≥0.
Show that E(X)=n+1n+2.
Show that Var(X)=n+1(n+2)2(n+3).
Markscheme
E(X)=(n+1)1∫0xn+1d M1
A1
leading to AG
[2 marks]
METHOD 1
use of M1
A1
M1
EITHER
A1
OR
A1
THEN
so AG
METHOD 2
use of M1
A1
M1
EITHER
A1
OR
A1
THEN
so AG
[6 marks]