6 In winter in Metland the weather each day can be classified as dry, wet or snowy. The table shows the probabilities for the next day's weather given the current day's weather.
| \cline { 3 - 5 }
\multicolumn{2}{c|}{} | next day's weather |
| \cline { 3 - 5 }
\multicolumn{2}{c|}{} | dry | wet | snowy |
| \multirow{3}{*}{} | dry | \(\frac { 4 } { 10 }\) | \(\frac { 3 } { 10 }\) | \(\frac { 3 } { 10 }\) |
| \cline { 2 - 5 } | wet | \(\frac { 2 } { 10 }\) | \(\frac { 5 } { 10 }\) | \(\frac { 3 } { 10 }\) |
| \cline { 2 - 5 } | snowy | \(\frac { 2 } { 7 }\) | \(\frac { 2 } { 7 }\) | \(\frac { 3 } { 7 }\) |
You are to use two-digit random numbers to simulate the winter weather in Metland.
- Give an efficient rule for using two-digit random numbers to simulate tomorrow's weather if today is
(A) dry,
(B) wet,
(C) snowy. - Today is a dry winter's day in Metland. Use the following two-digit random numbers to simulate the next 7 days' weather in Metland.
$$\begin{array} { l l l l l l l l l l }
23 & 85 & 98 & 99 & 56 & 47 & 82 & 14 & 03 & 12
\end{array}$$
- Use your simulation from part (ii) to estimate the proportion of dry days in a Metland winter.
- Explain how you could use simulation to produce an improved estimate of the proportion of dry days in a Metland winter.
- Give two criticisms of this model of weather.