OCR FS1 AS (Further Statistics 1 AS) 2021 June

1 A book reviewer estimates that the probability that he receives a delivery of books to review on any one weekday is 0.1 . The first weekday in September on which he receives a delivery of books to review is the \(X\) th weekday of September.

1. State an assumption needed for \(X\) to be well modelled by a geometric distribution.
2. Find \(\mathrm { P } ( X = 11 )\).
3. Find \(\mathrm { P } ( X \leqslant 8 )\).
4. Find \(\operatorname { Var } ( X )\).
5. Give a reason why a geometric distribution might not be an appropriate model for the first weekday in a calendar year on which the reviewer receives a delivery of books to review.

2 The probability distribution for the discrete random variable \(W\) is given in the table.

1. Show that \(\operatorname { Var } ( W ) = 0.8571\).
2. Find \(\operatorname { Var } ( 3 W + 6 )\). In this question you must show detailed reasoning.
   The random variable \(T\) has a binomial distribution. It is known that \(\mathrm { E } ( T ) = 5.625\) and the standard deviation of \(T\) is 1.875 . Find the values of the parameters of the distribution.

4 The table shows the results of a random sample drawn from a population which is thought to have the distribution \(\mathrm { U } ( 20 )\). \end{table}