Discrete random variables — Question 90
Original QCE Vault practice · 5 marks
Q90 · Practice questionTechnology-freeComplex familiar5 marks
QUESTION 90 (5 marks)
A discrete random variable X has P(X=x)=kx for x=1,2,3,4. Determine k, E(X) and Var(X). WORKED SOLUTION
Practice marking scheme
5 marksANSWERk=0.1, E(X)=3, Var(X)=1. Worked solution
k(1+2+3+4)=1 gives k=0.1. Then E(X)=0.1(1+4+9+16)=3 and E(X2)=0.1(1+8+27+64)=10, so Var(X)=10−9=1. Uses total probability to obtain k=0.1. Forms the expectation correctly.
Obtains E(X)=3. Obtains E(X2)=10. Obtains Var(X)=1. Practice question aligned to the current QCAA syllabus; review the worked solution and marking criteria.
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