Discrete random variables — Question 40
Original QCE Vault practice · 4 marks
Q40 · Practice questionTechnology-activeComplex familiar4 marks
QUESTION 40 (4 marks)
A game pays $0, $50 or $100 with probabilities 0.5, 0.3 and 0.2 respectively. Determine the fair entry price and the variance of the payout. WORKED SOLUTION
Practice marking scheme
4 marksANSWERFair price = $35; variance = 1525 dollars². Worked solution
E(X)=0(0.5)+50(0.3)+100(0.2)=35. Also E(X2)=2500(0.3)+10000(0.2)=2750, so Var(X)=2750−352=1525. Calculates E(X)=35. States the fair entry price as $35. Calculates E(X2)=2750. Determines the variance as 1525. Practice question aligned to the current QCAA syllabus; review the worked solution and marking criteria.
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