In 42 of the 64 years from 1950 through 2014,the S& P 500 finished higher after the first five days of trading (in 2011 there was virtually no change). In 37 out of 42 years, the S&P 500 finished higher for the year. Is a good first week a good omen for the upcoming year? The following table gives the first-week and annual performance over this 64-year period. S&P 500's Annual Performance First week Higher Lower Total Higher 37 5 42 Lower 11 11 22 Total 48 16 64 a) If a year is selected at random,what is the probability that the S&P 500 finished lower for the year? b) Given that the S&P fiished lowerr after the first five days of trading, what is the proability that it finished lower for the year? c) Are the two events "first week performance" and "annual performance" independent?
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!
In 42 of the 64 years from 1950 through 2014,the S& P 500 finished higher after the first five days of trading (in 2011 there was virtually no change). In 37 out of 42 years, the S&P 500 finished higher for the year. Is a good first week a good omen for the upcoming year? The following table gives the first-week and annual performance over this 64-year period.
| S&P 500's Annual Performance | |||
| First week | Higher | Lower | Total |
| Higher | 37 | 5 | 42 |
| Lower | 11 | 11 | 22 |
| Total | 48 | 16 | 64 |
a) If a year is selected at random,what is the
b) Given that the S&P fiished lowerr after the first five days of trading, what is the proability that it finished lower for the year?
c) Are the two
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