Date | November 2013 | Marks available | 6 | Reference code | 13N.1.hl.TZ0.2 |
Level | HL only | Paper | 1 | Time zone | TZ0 |
Command term | Find | Question number | 2 | Adapted from | N/A |
Question
The discrete random variable X has probability distribution:
(a) Find the value of a.
(b) Find E(X).
(c) Find Var(X).
Markscheme
(a) 16+12+310+a=1⇒a=130 A1
(b) E(X)=12+2×310+3×130 M1
=65 A1
Note: Do not award FT marks if a is outside [0, 1].
[2 marks]
(c) E(X2)=12+22×310+32×130=2 (A1)
attempt to apply Var(X)=E(X2)−(E(X))2 M1
(=2−3625)=1425 A1
[3 marks]
Total [6 marks]
Examiners report
This was very well answered and many fully correct solutions were seen. A small number of candidates made arithmetic mistakes in part a) and thus lost one or two accuracy marks. A few also seemed unaware of the formula Var(X)=E(X2)−E(X)2 and resorted to seeking an alternative, sometimes even attempting to apply a clearly incorrect Var(X)=∑(xi−μ)2.