4. Joint Probability Distribution Based on weather data from the morning of a da

Question

4. Joint Probability Distribution Based on weather data from the morning of a day, a prediction of the weather in the afternoon can be made. The following variables with probability values are given: S Sk clear clear clear clear cloudy cloudy cloudy PePressure rising rising falling falling rising rising falling WE WeatherlnAfternoon sunshine rain sunshine rain sunshine rain sunshine P(S,P,W) 0.40 0.07 0.08 0.10 0.09 0.11 0.03 a) How many events does this joint probability distribution have for the three variables? b) Calculate P(W-sunshinejS-clear,P-rising) c) Calculate P(W-rainlS-cloudy)

Explanation / Answer

ANSWERS::

FOR A:

There are 8 events for 3 variables

when S=clear P=raising/falling W=sunshine/rain =4

when S=cloudy P=raising/falling W=sunshine/rain =4

Total 8 events

FOR B:

P(W=sunshine| S=clear,P=rising)= 0.40/(0.40+0.08+0.09+0.03)=0.666

FOR C:

P(W=rain|S=cloudy) =0.11/(0.07+0.10+0.11)=0.392

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