A-Level MathematicsYear 2021Q6
18 6. The probability generating function of the random variable X is GX(t) = k(1 + 2t)5 where k is a constant. (a) Show that k = 1 243 (2) (b) Find P(X = 2) (2) (c) Find the probability generating function of W = 2X + 3 (2) The probability generating function of the random variable Y is GY(t) = t t ( ) 1 2 9 2 + Given that X and Y are independent, (d) find the probability generating function of U = X + Y in its simplest form. (2) (e) Use calculus to find the value of Var(U) (6) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________
Paper Source:9FM0_3B_que_20211016.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)