At Oak industries, Pokeballs will eventually fail. Each Pokeball costs $100. The time until failure is uniformly distributed on [0,4] (in years). If a Pokeball fails in the first year, Prof.Oak refunds the full purchase to the customer. If the ball fails in the second year, the refund is half of the full price. If the ball fails in the third year, the refund is 20% of the full price. There is no refund if the ball fails in the fourth year. What is the expected value and the standard deviation of the refund for a Pokeball?
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!
At Oak industries, Pokeballs will eventually fail. Each Pokeball costs $100. The time until failure is uniformly distributed on [0,4] (in years). If a Pokeball fails in the first year, Prof.Oak refunds the full purchase to the customer. If the ball fails in the second year, the refund is half of the full price. If the ball fails in the third year, the refund is 20% of the full price. There is no refund if the ball fails in the fourth year. What is the
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