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.
a) Write the probability distribution of next year’s profit for this farmer.
b) Construct the cumulative probability distribution of next year’s profit for this farmer.
c) Calculate the expected of next year’s profit in thousands of ringgits for this farmer. Give a brief interpretation of the value obtained.
d) Calculate the standard deviation of next year’s profit in thousands of ringgits for this farmer.
e) Discuss the meaning of standard deviation of the random variable focusing on the values obtained in (c) and (d) above.