A-Level MathematicsYear 2021Q5
16 5. The continuous random variable X is uniformly distributed over the interval [0, 4β ], where β is an unknown constant. Three independent observations, X1, X2 and X3 , are taken of X and the following estimators for β are proposed A = X X 1 2 2 + B = X X X 1 2 3 2 3 8 + + C = X X X 1 2 3 2 8 + − (a) Calculate the bias of A, the bias of B and the bias of C (5) (b) By calculating the variances, explain which of B or C is the better estimator for β (4) (c) Find an unbiased estimator for β (1) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________
Paper Source:9FM0_4B_que_20211023.pdf
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Exam Specification Info
This question is part of the UK A-Level Mathematics syllabus. In the actual exam, structured questions typically require linking specific keywords to gain full marks. Applaa helps you drill these topics.
Syllabus levelAdvanced Level (A-Level)
SubjectMathematics
Official MarksVariable (2–6 marks)