Discrete random variables — Question 364
Original QCE Vault practice · 4 marks
Q364 · Practice questionTechnology-freeSimple familiar4 marks
QUESTION 364 (4 marks)
Two independent-trial systems use success indicators A and B. For a single trial, P(A=1)=0.3 and P(B=1)=0.6. a)Determine the mean and variance of each indicator.
b)Compare their variability about their means. Explain your reasoning.
WORKED SOLUTION
Practice marking scheme
4 marksANSWERa) Means 0.3,0.6; variances 0.21,0.24. b) B is more variable about its mean. Worked solution
a) A success indicator is Bernoulli, with mean p and variance p(1−p). b) The variance 0.24 is larger than 0.21. Bernoulli variability is largest at p=0.5; 0.6 is closer to 0.5 than 0.3. Exact answers unless rounding is specified; equivalent forms accepted. Retain unrounded intermediate values.
Determines both variances.
Identifies B as more variable.
Justifies the comparison using variance.
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