A loss random variable X has a continuous uniform distribution on the interval (0, 100). An insurance policy on the loss pays the full amount of the loss if the loss is less than or equal to 40. If the loss is above 40 but less than or equal to 80, then the insurance pays 40 plus one-half of the loss in excess of 40. If the loss is above 80, the insurance pays 60. If Y denotes the amount paid by the insurance when a loss occurs, find the variance ofY. A) 1020 B) 1040 C) 1060 D) 1080 1110 3 3 3 E)
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
