1 A researcher wishes to find people who say that they support a specific plan. Each day the researcher interviews people at random, one after the other, until they find one person who says that they support this plan. The researcher does not then interview any more people that day. The total number of people interviewed on any one day is denoted by \(R\).

1. Assume that in fact \(1 \%\) of the population would say that they support the plan.
   1. State an appropriate distribution with which to model \(R\), giving the value(s) of any parameter(s).
   2. Find \(\mathrm { P } ( 50 < R \leqslant 150 )\). The researcher incorrectly believes that the variance of a random variable \(X\) with any discrete probability distribution is given by the formula \([ \mathrm { E } ( X ) ] ^ { 2 } - \mathrm { E } ( X )\).
2. Show that, for the type of distribution stated in part (a), they will obtain the correct value of the variance, regardless of the value(s) of the parameter(s).