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In: Statistics and Probability

One theory concerning the S&P 500 Index is that if it increases during the first five...

One theory concerning the S&P 500 Index is that if it increases during the first five trading days of the year, it is likely to increase during the entire year. From 1950 through 2013, the
S&P 500 Index had these early gains in 41 years (in 2011 there was virtually no change). In 36 of these 41 years, the S&P 500 Index increased for the entire year. Assuming that this indicator
is a random event with no predictive value, you would expect that the indicator would be correct 50% of the time. What is the probability
of the S&P 500 Index increasing in 36 or more years if the true probability of an increase in the S&P 500 Index is
a. 0.50?
b. 0.70?
c. 0.90?
d. Based on the results of (a) through (c), what do you think is the probability that the S&P 500 Index will increase if there is an early gain in the first five trading days of the year? Explain.

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orchestra answered 2 years ago
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