Consider a circular cone of radius 3 and height 5, which we view horizontally as pictured below. Our goal in this activity is to use a definite integral to determine the volume of the cone. y=ƒ(x) (a) Find a formula for the linear function y = f(x) that is pictured above. f(x) = (b) For the representative slice of thickness Ax that is located horizontally at a location x (somewhere between x = the radius r of the representative slice? Note :0 and x = 5), what is that the radius depends on the value of x. r = (c) What is the volume Vslice (x) of the representative slice you found in (b)? (Use D as the value for Ax) slice (x):
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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