Consider the following problem where we work for an oil company that looks for oil in geographic formations that are favorable to the formation of oil. Find the expected value for barrels of oil in problem A and then find the variance and standard deviation. For B, find the mean, variance, and standard deviation using formulas. For variance and standard deviation, use the population formulas. Compare A and B, and what do you observe? Problem A Problem B Problem. A Oil (barrel) Odds Problem. B Oil (barrel) · Odds 2 25% · 2 · 25% 4 25% · 4 · 25% 4 25% · 4 · 25% 2 25% · 6 · 25%
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!
Consider the following problem where we work for an oil company that looks for oil in geographic formations that are favorable to the formation of oil. Find the
- Problem A Problem B
|
Problem. A Oil (barrel) |
Odds |
Problem. B Oil (barrel) |
·
Odds |
|
2 |
25% |
· 2 |
· 25% |
|
4 |
25% |
· 4 |
· 25% |
|
4 |
25% |
· 4 |
· 25% |
|
2 |
25% |
· 6 |
· 25% |
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