You are observing the speeds of two CPUs, to find which one is expected to run faster. After a number of observations, you came up with the following results: CPU Speed Measurements 37 38 40 35 30 31 26 25 Number of Observations 18 15 CPU 1 CPU 2 10 10 10 5 0 2.0-24 2.5-2.9 3.5 - 3.9 4.0 - 4.5 3.0-3.4 Speed (GHz) A. Using this data, calculate the expected speed of each processor, and determine which of the two is faster. (Hint: when given a range of speeds, you can consider the average value within that range to be the speed at which the observations occurred).
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!
You are observing the speeds of two CPUs, to find which one is expected to run faster. After a number of observations, you came up with the following results: CPU Speed Measurements 37 38 40 35 30 31 26 25 Number of Observations 18 15 CPU 1 CPU 2 10 10 10 5 0 2.0-24 2.5-2.9 3.5 - 3.9 4.0 - 4.5 3.0-3.4 Speed (GHz) A. Using this data, calculate the expected speed of each processor, and determine which of the two is faster. (Hint: when given a
Use the given data to form a table:
| Speed | CPU 1(F1) | CPU 2(F2) | Speed (x) | x*F1 | x*F2 |
| 2.0 to 2.4 | 15 | 8 | 2.2 | 33 | 17.6 |
| 2.5 to 2.9 | 26 | 37 | 2.7 | 70.2 | 99.9 |
| 3.0 to 3.4 | 31 | 38 | 3.2 | 99.2 | 121.6 |
| 3.5 to 3.9 | 18 | 10 | 3.7 | 66.6 | 37 |
| 4.0 to 4.5 | 10 | 7 | 4.25 | 42.5 | 29.75 |
| Sum | 100 | 100 | 311.5 | 305.85 |
Determine the expected value using the table:
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