Worksheet library · A Level
Further Statistics A Level Further Maths Worksheets, Questions and Revision
6 original Further Statistics worksheet packs - 66 printable pages with full mark schemes. Discrete random variables, hypothesis testing and chi-squared tests. View any pack in the browser or open the print-ready PDF.
See the method: Further Statistics: Discrete Random Variables and Expectation
The random variable X has probability distribution given in the table below, where P(X=3) = k. x: 1, 2, 3, 4. P(X=x): 1/10, 3/10, k, 1/4. (a) Find k. (b) Find E(X) and Var(X). (c) Given that Y = 3X - 2, find E(Y).
- Use sum P(X=x) = 1: 1/10 + 3/10 + k + 1/4 = 1. Writing every fraction as twentieths gives 2/20 + 6/20 + k + 5/20 = 1.
- Solve for k: 13/20 + k = 1, so k = 7/20.
- Find E(X) = sum x*P(X=x) = 1(2/20) + 2(6/20) + 3(7/20) + 4(5/20) = (2+12+21+20)/20 = 55/20 = 11/4.
- Find E(X^2) = sum x^2*P(X=x) = 1(2/20) + 4(6/20) + 9(7/20) + 16(5/20) = (2+24+63+80)/20 = 169/20.
- Use Var(X) = E(X^2) - [E(X)]^2 = 169/20 - (11/4)^2 = 169/20 - 121/16 = 676/80 - 605/80 = 71/80.
- Use E(aX+b) = aE(X)+b for part (c): E(Y) = 3(11/4) - 2 = 33/4 - 8/4 = 25/4. Final answer: k = 7/20, E(X) = 11/4, Var(X) = 71/80, E(Y) = 25/4.
2.1 Further Statistics: Discrete Random Variables and Expectation4p + answers · 115 marks · PDF
2.2 Further Statistics: Poisson and Geometric Distributions4p + answers · 111 marks · PDF
2.3 Further Statistics: Chi-Squared Tests (Goodness of Fit and Contingency Tables)8p + answers · 140 marks · PDF
2.4 Further Statistics: Hypothesis Testing, Type I and Type II Errors5p + answers · 101 marks · PDF
2.5 Further Statistics: Discrete Distributions Depth4p + answers · 94 marks · PDF
2.6 Further Statistics: Hypothesis Testing and Chi-Squared Depth9p + answers · 122 marks · PDF
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