| Date | None Specimen | Marks available | 3 | Reference code | SPNone.1.hl.TZ0.4 |
| Level | HL only | Paper | 1 | Time zone | TZ0 |
| Command term | Determine | Question number | 4 | Adapted from | N/A |
Question
The continuous variable X has probability density function
f(x)={12x2(1−x),0⩽
Determine {\text{E}}(X) .
[3]
a.
Determine the mode of X .
[3]
b.
Markscheme
{\text{E}}(X) = \int_0^1 {12{x^3}(1 - x){\text{d}}x} M1
= 12\left[ {\frac{{{x^4}}}{4} - \frac{{{x^5}}}{5}} \right]_0^1 A1
= \frac{3}{5} A1
[3 marks]
a.
f'(x) = 12(2x - 3{x^2}) A1
at the mode f'(x) = 12(2x - 3{x^2}) = 0 M1
therefore the mode = \frac{2}{3} A1
[3 marks]
b.
Examiners report
[N/A]
a.
[N/A]
b.
