Over a period of 100 days, weather forecasters issue forecasts for rain on a daily basis. Based on the forecasts and actual observations, you are supposed to help them ﬁnding out if the forecasts were any good. A forecast is simply one of the following three possible statements: “no rain”, “maybe rain”, or “certainly rain”. The forecasters record the number of days they issued each of these three forecasts, and also the corresponding number of days it rained. The results are collected below:
Forecast: "No rain" , Days with rain: 4, Days without rain: 18
Forecast: "Maybe rain" , Days with rain: 25, Days without rain: 22
Forecast: "Rain" , Days with rain: 25, Days without rain: 6
Show that has a multinomial distribution with unknown probabilities , which are the unknowns parameters in this problem. Write down the likelihood of the data as a function of and N.
This is a past exam paper and I have no clue how to answer this in a way that could get me marks! I've written the multinomial distribution:
But I can't work out how to do this question for the life of me! Can anyone help?