To aid engineers seeking to predict the efficiency of a solar-powered device, Olseth and Skartveit developed a model for daily insolation Y at sea-level locations within the temperate storm belt. To account for both “clear sky” and “overcast” days, the researchers constructed a probability density function for Y using a linear combination of two modified gamma distributions:

where

λ₁ = mean insolation of “clear sky” days

λ₂ = insolation of “cloudy” days

and w is a weighting constant, 0 ≤ w ≤ 1. Show that

Transcribed Image Text:

fy) = wg(y, A1) + (1 - w)g(1 – y, A2), (0 < y < 1)