Discrete random variables — Question 363
Original QCE Vault practice · 4 marks
Q363 · Practice questionTechnology-freeSimple familiar4 marks
QUESTION 363 (4 marks)
A kiosk records the number X of additional items bought in 60 transactions. xFrequency01812421236 Use relative frequencies as estimates of the probabilities.
a)Estimate P(1≤X≤2). b)Determine the estimated mean and variance of X. WORKED SOLUTION
Practice marking scheme
4 marksANSWERa) 0.6. b) E(X)=1.1 and Var(X)=0.89. Worked solution
a) The estimate is (24+12)/60=0.6. b) Probabilities are 0.3,0.4,0.2,0.1. E(X)=0.4+0.4+0.3=1.1 and E(X2)=0.4+0.8+0.9=2.1, giving variance 2.1−1.12=0.89. Exact answers unless rounding is specified; equivalent forms accepted. Retain unrounded intermediate values.
Uses the correct combined frequencies.
Constructs the empirical probability distribution.
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