Question: This exercise asks you to explore the joint statistical distribution of the S&P 500 index and the Nasdaq Index. You should proceed as follows. Go

This exercise asks you to explore the joint statistical distribution of the S&P 500 index and the Nasdaq Index. You should proceed as follows.

Go to https://finance.yahoo.com and download the daily data for the S&P index and for the Nasdaq index for the last year. In particular, you will have the closing value of the index for each trading day.

Compute the series of daily returns for both indices as done in Home- work 2.

For each series, compute mean, median, 0.25-quantile, 0.75-quantile and standard deviation. Produce a picture showing the probability distribution of the returns. Produce a picture showing the cumulative distribution function of the returns.

Compute the correlation coefficient for the two indices.

Compute the conditional probability that the daily return on the Nas- daq is positive given that the return on the S&P is negative.

Nasdaq data:

Date

Open

High

Low

Close

10/18/2021

14,839.74

15,026.68

14,833.28

15,021.81

10/15/2021

14,891.24

14,904.98

14,847.97

14,897.34

10/14/2021

14,717.50

14,827.56

14,699.53

14,823.43

10/13/2021

14,537.17

14,589.28

14,471.88

14,571.64

10/12/2021

14,539.09

14,552.71

14,441.60

14,465.92

10/11/2021

14,540.08

14,665.99

14,482.62

14,486.20

10/8/2021

14,694.72

14,699.91

14,569.68

14,579.54

10/7/2021

14,631.80

14,755.72

14,615.14

14,654.02

10/6/2021

14,289.45

14,509.55

14,259.07

14,501.91

10/5/2021

14,312.86

14,508.65

14,299.78

14,433.83

10/4/2021

14,493.12

14,499.74

14,181.69

14,255.48

10/1/2021

14,494.93

14,606.82

14,324.01

14,566.70

9/30/2021

14,582.60

14,632.36

14,444.30

14,448.58

9/29/2021

14,614.88

14,676.62

14,493.67

14,512.44

9/28/2021

14,787.21

14,817.74

14,539.88

14,546.68

9/27/2021

14,954.18

15,003.16

14,864.96

14,969.97

9/24/2021

14,961.62

15,067.56

14,946.57

15,047.70

9/23/2021

14,960.00

15,085.44

14,932.52

15,052.24

9/22/2021

14,800.59

14,950.12

14,767.02

14,896.85

9/21/2021

14,803.36

14,847.03

14,696.47

14,746.40

9/20/2021

14,758.14

14,841.82

14,530.07

14,713.90

9/17/2021

15,163.36

15,166.56

14,998.73

15,043.97

9/16/2021

15,120.09

15,205.50

15,047.14

15,181.92

9/15/2021

15,071.34

15,174.38

14,984.68

15,161.53

9/14/2021

15,168.45

15,181.19

15,008.30

15,037.76

9/13/2021

15,211.43

15,215.44

15,030.85

15,105.58

9/10/2021

15,332.92

15,349.47

15,111.31

15,115.49

9/9/2021

15,296.06

15,352.38

15,245.18

15,248.25

9/8/2021

15,360.35

15,360.34

15,206.61

15,286.64

9/7/2021

15,375.98

15,403.44

15,343.28

15,374.33

9/3/2021

15,313.41

15,375.56

15,283.67

15,363.52

9/2/2021

15,358.47

15,380.07

15,285.35

15,331.18

9/1/2021

15,308.98

15,379.50

15,302.11

15,309.38

8/31/2021

15,262.88

15,278.96

15,202.67

15,259.24

8/30/2021

15,165.94

15,288.08

15,165.12

15,265.89

8/27/2021

14,969.77

15,144.48

14,966.52

15,129.50

8/26/2021

15,025.17

15,059.63

14,939.56

14,945.81

8/25/2021

15,039.03

15,059.43

15,011.58

15,041.86

8/24/2021

14,978.14

15,034.89

14,965.54

15,019.80

8/23/2021

14,776.98

14,963.47

14,776.98

14,942.65

8/20/2021

14,571.53

14,722.16

14,571.53

14,714.66

8/19/2021

14,423.16

14,610.76

14,423.16

14,541.79

8/18/2021

14,636.24

14,697.25

14,516.30

14,525.91

8/17/2021

14,670.56

14,716.95

14,550.88

14,656.18

8/16/2021

14,771.53

14,794.68

14,610.02

14,793.76

8/13/2021

14,825.07

14,850.61

14,797.22

14,822.90

8/12/2021

14,751.36

14,824.31

14,698.94

14,816.26

8/11/2021

14,834.38

14,842.50

14,692.41

14,765.14

8/10/2021

14,887.75

14,894.61

14,754.48

14,788.09

8/9/2021

14,855.76

14,883.81

14,802.69

14,860.18

8/6/2021

14,864.22

14,890.18

14,788.59

14,835.76

8/5/2021

14,794.08

14,896.47

14,776.03

14,895.12

8/4/2021

14,747.21

14,812.38

14,734.12

14,780.53

8/3/2021

14,714.00

14,762.60

14,584.09

14,761.29

8/2/2021

14,758.60

14,770.41

14,665.67

14,681.07

7/30/2021

14,615.85

14,728.79

14,615.85

14,672.68

7/29/2021

14,771.17

14,833.74

14,761.38

14,778.26

7/28/2021

14,715.66

14,798.88

14,645.63

14,762.58

7/27/2021

14,807.95

14,811.08

14,503.75

14,660.58

7/26/2021

14,821.03

14,863.65

14,790.49

14,840.71

7/23/2021

14,753.06

14,846.06

14,698.77

14,836.99

7/22/2021

14,652.72

14,694.19

14,617.87

14,684.60

7/21/2021

14,508.75

14,633.15

14,498.65

14,631.95

7/20/2021

14,330.46

14,555.75

14,271.23

14,498.88

7/19/2021

14,235.98

14,313.59

14,178.66

14,274.98

7/16/2021

14,597.51

14,623.02

14,413.32

14,427.24

7/15/2021

14,635.78

14,650.38

14,451.80

14,543.13

7/14/2021

14,780.90

14,790.55

14,632.95

14,644.95

7/13/2021

14,715.13

14,803.68

14,660.19

14,677.65

7/12/2021

14,743.86

14,761.08

14,672.63

14,733.24

7/9/2021

14,578.43

14,710.20

14,552.26

14,701.92

7/8/2021

14,409.20

14,610.06

14,371.59

14,559.78

7/7/2021

14,753.42

14,755.33

14,580.79

14,665.06

7/6/2021

14,661.55

14,687.00

14,529.80

14,663.64

7/2/2021

14,582.98

14,649.11

14,555.34

14,639.33

7/1/2021

14,493.69

14,533.55

14,439.40

14,522.38

6/30/2021

14,509.85

14,526.81

14,478.06

14,503.95

6/29/2021

14,509.19

14,535.97

14,471.38

14,528.33

6/28/2021

14,417.81

14,505.19

14,417.20

14,500.51

6/25/2021

14,400.81

14,409.08

14,337.65

14,360.39

6/24/2021

14,357.27

14,414.46

14,333.70

14,369.71

6/23/2021

14,263.38

14,317.66

14,246.30

14,271.73

6/22/2021

14,138.29

14,269.77

14,121.00

14,253.27

6/21/2021

14,047.42

14,150.78

13,960.04

14,141.48

6/18/2021

14,096.93

14,129.22

14,009.04

14,030.38

6/17/2021

13,999.13

14,196.21

13,998.93

14,161.35

6/16/2021

14,085.55

14,129.69

13,903.73

14,039.68

6/15/2021

14,166.64

14,171.02

14,052.16

14,072.86

6/14/2021

14,083.47

14,175.45

14,056.67

14,174.14

6/11/2021

14,030.85

14,069.42

14,006.59

14,069.42

6/10/2021

13,933.88

14,031.19

13,904.40

14,020.33

6/9/2021

13,980.23

14,003.50

13,906.45

13,911.75

6/8/2021

13,946.32

13,981.72

13,831.98

13,924.91

6/7/2021

13,802.82

13,889.11

13,784.89

13,881.72

6/4/2021

13,697.25

13,826.82

13,692.01

13,814.49

6/3/2021

13,655.75

13,684.13

13,548.93

13,614.51

6/2/2021

13,743.24

13,775.90

13,689.73

13,756.33

6/1/2021

13,829.06

13,836.17

13,678.77

13,736.48

5/28/2021

13,792.05

13,820.87

13,747.61

13,748.74

5/27/2021

13,742.59

13,776.52

13,701.63

13,736.28

5/26/2021

13,693.94

13,750.16

13,679.59

13,738.00

5/25/2021

13,721.54

13,751.14

13,631.80

13,657.17

5/24/2021

13,557.21

13,708.85

13,551.01

13,661.17

5/21/2021

13,616.19

13,616.58

13,463.27

13,470.99

5/20/2021

13,356.63

13,563.52

13,355.71

13,535.74

5/19/2021

13,078.19

13,304.61

13,072.23

13,299.74

5/18/2021

13,416.90

13,485.34

13,299.93

13,303.64

5/17/2021

13,368.80

13,399.17

13,265.40

13,379.05

5/14/2021

13,255.65

13,460.88

13,242.97

13,429.98

5/13/2021

13,150.94

13,247.88

13,007.24

13,124.99

5/12/2021

13,215.49

13,288.61

13,002.54

13,031.68

5/11/2021

13,115.85

13,423.31

13,107.67

13,389.43

5/10/2021

13,687.60

13,687.93

13,401.75

13,401.86

5/7/2021

13,723.09

13,828.62

13,690.75

13,752.24

5/6/2021

13,557.83

13,635.73

13,439.39

13,632.84

5/5/2021

13,731.13

13,753.05

13,553.93

13,582.42

5/4/2021

13,774.51

13,795.57

13,485.59

13,633.50

5/3/2021

14,031.77

14,042.13

13,881.51

13,895.12

4/30/2021

13,970.73

14,084.76

13,941.63

13,962.68

4/29/2021

14,204.52

14,211.57

13,952.80

14,082.55

4/28/2021

14,082.78

14,133.65

14,034.70

14,051.03

4/27/2021

14,170.91

14,171.24

14,064.28

14,090.22

4/26/2021

14,052.38

14,154.03

14,019.50

14,138.78

4/23/2021

13,861.37

14,062.73

13,856.83

14,016.81

4/22/2021

13,952.57

14,015.87

13,771.04

13,818.41

4/21/2021

13,745.77

13,951.35

13,706.86

13,950.22

4/20/2021

13,894.46

13,927.67

13,698.67

13,786.27

4/19/2021

13,984.58

14,041.79

13,842.57

13,914.77

4/16/2021

14,059.11

14,062.50

13,977.05

14,052.34

4/15/2021

13,983.23

14,049.13

13,970.42

14,038.76

4/14/2021

14,004.08

14,033.63

13,839.04

13,857.84

4/13/2021

13,902.45

14,011.51

13,902.45

13,996.10

4/12/2021

13,854.44

13,877.00

13,783.95

13,850.00

4/9/2021

13,787.02

13,905.41

13,748.35

13,900.19

4/8/2021

13,796.89

13,830.14

13,758.71

13,829.31

4/7/2021

13,675.30

13,733.03

13,653.59

13,688.84

4/6/2021

13,681.67

13,776.71

13,674.28

13,698.38

4/5/2021

13,705.59

13,720.58

13,582.76

13,705.59

4/1/2021

13,414.32

13,487.08

13,404.18

13,480.11

3/31/2021

13,122.57

13,325.54

13,118.38

13,246.87

3/30/2021

13,008.80

13,075.75

12,922.57

13,045.39

3/29/2021

13,103.97

13,143.41

12,968.16

13,059.65

3/26/2021

12,996.03

13,149.55

12,878.72

13,138.72

3/25/2021

12,844.58

13,021.86

12,786.81

12,977.68

3/24/2021

13,289.24

13,292.92

12,961.35

12,961.89

3/23/2021

13,381.44

13,405.15

13,202.43

13,227.70

3/22/2021

13,278.78

13,455.65

13,278.78

13,377.54

3/19/2021

13,119.90

13,252.37

13,039.45

13,215.24

3/18/2021

13,349.20

13,384.46

13,101.93

13,116.17

3/17/2021

13,336.92

13,595.00

13,272.69

13,525.20

3/16/2021

13,523.17

13,620.71

13,397.09

13,471.57

3/15/2021

13,323.47

13,460.35

13,272.50

13,459.71

3/12/2021

13,222.81

13,324.70

13,158.72

13,319.86

3/11/2021

13,273.31

13,433.62

13,246.32

13,398.67

3/10/2021

13,234.73

13,277.11

13,035.44

13,068.83

3/9/2021

12,923.07

13,151.54

12,882.49

13,073.82

3/8/2021

12,904.26

13,001.00

12,599.23

12,609.16

3/5/2021

12,860.04

12,941.22

12,397.06

12,920.15

3/4/2021

12,953.99

13,068.71

12,553.96

12,723.47

3/3/2021

13,336.25

13,372.52

12,995.07

12,997.75

3/2/2021

13,599.45

13,601.33

13,352.00

13,358.79

3/1/2021

13,406.16

13,596.59

13,362.66

13,588.83

2/26/2021

13,232.90

13,368.06

13,024.53

13,192.35

2/25/2021

13,512.64

13,602.86

13,066.38

13,119.43

2/24/2021

13,400.25

13,607.36

13,286.59

13,597.97

2/23/2021

13,262.61

13,526.09

13,003.98

13,465.20

2/22/2021

13,714.20

13,757.06

13,530.96

13,533.05

2/19/2021

13,929.20

13,985.58

13,842.59

13,874.46

2/18/2021

13,814.67

13,905.96

13,714.35

13,865.36

2/17/2021

13,911.65

13,976.43

13,804.26

13,965.49

2/16/2021

14,152.22

14,175.11

13,995.45

14,047.50

2/12/2021

13,979.21

14,102.04

13,937.71

14,095.47

2/11/2021

14,045.21

14,058.91

13,916.84

14,025.77

2/10/2021

14,093.35

14,109.12

13,845.47

13,972.53

2/9/2021

13,966.82

14,044.95

13,966.56

14,007.70

2/8/2021

13,937.06

13,987.74

13,894.15

13,987.64

2/5/2021

13,824.88

13,878.16

13,761.66

13,856.30

2/4/2021

13,674.06

13,778.42

13,631.62

13,777.74

2/3/2021

13,718.32

13,723.83

13,585.34

13,610.54

2/2/2021

13,543.10

13,652.70

13,535.86

13,612.78

2/1/2021

13,226.18

13,431.46

13,132.47

13,403.39

1/29/2021

13,284.72

13,322.00

12,985.05

13,070.69

1/28/2021

13,323.30

13,507.64

13,316.52

13,337.16

1/27/2021

13,486.58

13,538.42

13,192.91

13,270.60

1/26/2021

13,681.72

13,702.69

13,603.19

13,626.06

1/25/2021

13,681.21

13,728.98

13,368.68

13,635.99

1/22/2021

13,474.81

13,567.14

13,463.66

13,543.06

1/21/2021

13,521.48

13,560.35

13,454.07

13,530.91

1/20/2021

13,342.55

13,486.13

13,329.77

13,457.25

1/19/2021

13,132.73

13,206.86

13,078.70

13,197.18

1/15/2021

13,099.90

13,139.83

12,949.76

12,998.50

1/14/2021

13,174.76

13,220.16

13,098.41

13,112.64

1/13/2021

13,088.01

13,171.15

13,051.07

13,128.95

1/12/2021

13,062.06

13,105.04

12,963.92

13,072.43

1/11/2021

13,048.78

13,138.27

12,999.51

13,036.43

1/8/2021

13,160.22

13,208.09

13,036.55

13,201.98

1/7/2021

12,867.34

13,090.91

12,867.34

13,067.48

1/6/2021

12,666.15

12,909.63

12,649.99

12,740.79

1/5/2021

12,665.65

12,828.27

12,665.65

12,818.96

1/4/2021

12,958.52

12,958.73

12,543.24

12,698.45

12/31/2020

12,877.09

12,902.07

12,821.23

12,888.28

12/30/2020

12,906.51

12,924.93

12,857.76

12,870.00

12/29/2020

12,965.39

12,973.33

12,821.97

12,850.22

12/28/2020

12,914.64

12,930.89

12,827.45

12,899.42

12/24/2020

12,791.54

12,833.55

12,767.64

12,804.73

12/23/2020

12,834.94

12,841.92

12,758.67

12,771.11

12/22/2020

12,785.22

12,840.57

12,695.31

12,807.92

12/21/2020

12,596.14

12,751.27

12,525.22

12,742.52

12/18/2020

12,804.93

12,809.60

12,654.61

12,755.64

12/17/2020

12,730.78

12,765.25

12,696.35

12,764.75

12/16/2020

12,611.04

12,687.32

12,566.38

12,658.19

12/15/2020

12,543.26

12,596.13

12,465.42

12,595.06

12/14/2020

12,447.44

12,543.00

12,432.71

12,440.04

12/11/2020

12,336.79

12,383.50

12,246.77

12,377.87

12/10/2020

12,247.55

12,431.56

12,214.74

12,405.81

12/9/2020

12,591.69

12,607.15

12,290.78

12,338.95

12/8/2020

12,503.17

12,594.54

12,453.21

12,582.77

12/7/2020

12,461.00

12,536.23

12,460.55

12,519.95

12/4/2020

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12,464.23

12,376.44

12,464.23

12/3/2020

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12,439.02

12,356.98

12,377.18

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12,285.75

12,360.06

12,217.35

12,349.37

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12,405.79

12,263.93

12,355.11

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12,244.65

12,027.16

12,198.74

11/27/2020

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12,236.23

12,154.57

12,205.85

11/25/2020

12,053.89

12,114.77

12,020.95

12,094.40

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11,939.33

12,049.88

11,863.45

12,036.79

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11,916.76

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11,796.53

11,880.63

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11,892.70

11,935.47

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11,779.04

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11,760.98

11,904.71

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11,896.06

11,942.49

11,799.96

11,801.60

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11,913.35

11,950.18

11,852.41

11,899.34

11/16/2020

11,847.11

11,937.72

11,814.89

11,924.13

11/13/2020

11,794.94

11,849.79

11,715.52

11,829.29

11/12/2020

11,802.50

11,847.84

11,666.38

11,709.59

11/11/2020

11,656.65

11,793.57

11,638.90

11,786.43

11/10/2020

11,622.44

11,665.87

11,424.61

11,553.86

11/9/2020

12,046.66

12,108.07

11,703.49

11,713.78

11/6/2020

11,869.90

11,920.54

11,737.13

11,895.23

11/5/2020

11,816.33

11,924.28

11,784.15

11,890.93

11/4/2020

11,443.78

11,663.31

11,394.21

11,590.78

11/3/2020

11,038.66

11,213.92

11,004.84

11,160.57

11/2/2020

11,010.45

11,071.08

10,830.95

10,957.61

10/30/2020

11,103.47

11,129.81

10,822.57

10,911.59

10/29/2020

11,064.47

11,287.63

11,030.19

11,185.59

10/28/2020

11,230.90

11,249.95

10,999.07

11,004.87

10/27/2020

11,409.34

11,465.06

11,361.86

11,431.35

10/26/2020

11,440.64

11,545.63

11,221.06

11,358.94

10/23/2020

11,536.01

11,548.85

11,434.86

11,548.28

10/22/2020

11,526.98

11,548.77

11,369.29

11,506.01

10/21/2020

11,530.39

11,613.79

11,476.08

11,484.69

10/20/2020

11,531.83

11,632.89

11,471.23

11,516.49

10/19/2020

11,732.34

11,778.11

11,454.57

11,478.88

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