Is the Stock Market Independent? The Standard and Poor 500 (S&P 500) is a weighted average...

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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. Your answer is correct. (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. P(increase) 0.5595 eTextbook and Media Hint Your answer is partially correct. (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. P(increases for two consecutive days) = 0.3131 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. P(increases on a day if increased the day before) = i eTextbook and Media Hint Assistance Used 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. Your answer is correct. (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. P(increase) 0.5595 eTextbook and Media Hint Your answer is partially correct. (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. P(increases for two consecutive days) = 0.3131 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. P(increases on a day if increased the day before) = i eTextbook and Media Hint Assistance Used