In a certain city the daily consumption of water (inmillions of liters) is a random variable whose probabilitydensity is given by f(x) =⎧⎪⎪⎨⎪⎪⎩19xe− x3 for x > 00 elsewhereWhat are the probabilities that on a given day(a) the water consumption in this city is no more than 6million liters;(b) the water supply is inadequate if the daily capacity ofthis city is 9 million liters?
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!
millions of liters) is a random variable whose probability
density is given by
⎧
⎪⎪⎨
⎪⎪⎩
1
9
xe− x
3 for x > 0
0 elsewhere
What are the probabilities that on a given day
(a) the water consumption in this city is no more than 6
million liters;
(b) the water supply is inadequate if the daily capacity of
this city is 9 million liters?
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