how to answer it?

Question

A farmer will earn a profit of RM28,000 in case of heavy rain next year, RM55,000 in case of moderate rain, RM15,000 in case of little rain, and RM7,000 in case of no rain. A meteorologist forecasts that the probability is 0.30 for heavy rain, 0.35 for moderate rain, 0.20 for little rain, and 0.15 for no rain next year.

Answer 1

Split the range (RM55000-7000=RM48000) into 4 equal bands. These bands correspond to no rain, little rain, moderate rain, heavy rain. Construct a histogram representing the percentages in steps of 5%: 5, 10, 15, 20, 25, 30, 35 and the heights of the blocks for the four rain or profit bands will be 15, 20, 35, 30. The histogram represents the probability distribution. Label the percentage points with the corresponding profit: 7, 15, 55 and 28 (representing RM000's). From the histogram it's easy to see, for example, that to make a profit of RM20,000 there needs to be light to moderate rainfall, and there's more than a 20% probability of that eventuality. The total area of the histogram blocks represents 100% and illustrates cumulative distribution. There is, for example, 70% probability that rainfall will not be heavy and 85% probability that there will be some rain (that's 85% probability that profit will be at least RM15,000). The histogram is biased towards moderate to heavy rainfall for maximum profit.