Is the Stock Market Independent?The Standard and Poor 500 (S&P 500) is a weighted average of the stocks for 500 large companies in the United States. It is commonly used as a measure of the overall performance of the US stock market. Between January 1, 2009 and January 1, 2012, the S&P 500 increased for 423 of the 756 days that the stock market was open. We will investigate whether changes to the S&P 500 are independent from day to day. This is important, because if changes are not independent, we should be able to use the performance on the current day to help predict performance on the next day.     (a) What is the probability that the S&P 500 increased on a randomly selected market day between January 1, 2009 and January 1, 2012?Round your answer to four decimal places.  (b) If we assume that daily changes to the S&P 500 are independent, what is the probability that the S&P 500 increases for two consecutive days?Round your answer to four decimal places. What is the probability that the S&P 500 increases on a day, given that it increased the day before?Round your answer to four decimal places. (c) Between January 1, 2009 and January 1, 2012 the S&P 500 increased on two consecutive market days 234 times out of a possible 755. Based on this information, what is the probability that the S&P 500 increases for two consecutive days?Round your answer to four decimal places. What is the probability that the S&P 500 increases on a day, given that it increased the day before?Round your answer to four decimal places.

Question
Is the Stock Market Independent?

The Standard and Poor 500 (S&P 500) is a weighted average of the stocks for 500 large companies in the United States. It is commonly used as a measure of the overall performance of the US stock market. Between January 1, 2009 and January 1, 2012, the S&P 500 increased for 423 of the 756 days that the stock market was open. We will investigate whether changes to the S&P 500 are independent from day to day. This is important, because if changes are not independent, we should be able to use the performance on the current day to help predict performance on the next day.
 
 
(a) What is the probability that the S&P 500 increased on a randomly selected market day between January 1, 2009 and January 1, 2012?

Round your answer to four decimal places.
 (b) If we assume that daily changes to the S&P 500 are independent, what is the probability that the S&P 500 increases for two consecutive days?

Round your answer to four decimal places.
What is the probability that the S&P 500 increases on a day, given that it increased the day before?

Round your answer to four decimal places.
(c) Between January 1, 2009 and January 1, 2012 the S&P 500 increased on two consecutive market days 234 times out of a possible 755. Based on this information, what is the probability that the S&P 500 increases for two consecutive days?

Round your answer to four decimal places.
What is the probability that the S&P 500 increases on a day, given that it increased the day before?

Round your answer to four decimal places.

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