(Solved): Part ii PART B) The Wikipedia List of countries and dependencies by population gives the number of p ...

PART B) The Wikipedia List of countries and dependencies by population gives the number of people living in each of 250 countries and dependencies. The following table records the number of countries whose population figure begins with the digit \( \mathrm{i} \), for \( 1 \leq i \leq 9 \) : For example, the population of Denmark is listed as \( 5,707,251 \) and so it is one of the 24 countries whose population has first digit 5. i) If first digits are selected uniformly at random from \( \{1,2, \ldots, 9\} \) what is the probability distribution of the random variable \( X_{i} \) that represents the number of countries whose population has first digit \( i \) ? [3 marks] ii) Are the first digits uniformly distributed? Perform a \( \chi^{2} \) goodness of fit test. [7 marks]