Suppose you are in a treehouse 92 feet above the ground. You want to raise a bucket of water from the ground to the treehouse with a small rope. The bucket weighs 10 lb, and it has 24 lb of water in it. The rope weighs 1 Ib. Once you begin pulling the bucket of water up to the treehouse, water leaks at a constant rate out of a hole in the bottom of the bucket. When the bucket reaches the treehouse, the last of the water leaks from the bucket. How much work was used to pull the bucket (now empty) up to the treehouse?
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!
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