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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=1a=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

(=23625)=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)=(xiμ)2.

Syllabus sections

Topic 5 - Core: Statistics and probability » 5.5 » Concept of discrete and continuous random variables and their probability distributions.

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