Is she empirically well calibrated? What is her daily average Brier score? Please show work.

3. Over a period of 100 days a weather forecaster quotes probability forecasts q = 0.1, 0.3, 0.5, 0.7, 0.9 on n[q] occasions, it raining on r[q] of those days. Her results are given below. q 0.1 0.3 0.5 0.7 0.9 r[q] 4 9 5 14 15 n[q] 20 30 10 20 20 Is she empirically well calibrated? What's her empirical daily average Brier score? Recall that the Brier score loss function for any given day is L(a, q) = (a - q)2 where a = I{rain that day} and q is the quoted forecast for rain for that day