• (HW_1_1)  The clearness index was determined for the skies over Baghdad for each of the 365 days during a particular year. It was a contribution to the study of the solar radiation of the Baghdad environment. The following table summarized the resulting data.

• Determine the Relative Frequency and the Cumulative Relative Frequency (fill in the two last columns of the table)
• Sketch the Relative Frequency histogram and comment on it (use: http://dostat.stat.sc.edu/webstat/3.0/oldindex.html, copy the second column frequencies and  paste them in the Data link. Then Go to Graphs and plot the relative frequencies. Save the graph and include in your HW document.)
  
• Visually choose a model distribution from http://socr.stat.ucla.edu/test/SOCR_Distributions.html, compute and enter the corresponding model probabilities for each range in the last column (by varying the left & right limit of the regions using mouse clicks).
  
• Cloudy days are those with the clearness index < 0.35. What proportion of the days were cloudy? How different are the data and model probabilities?
  
• Clear days are those for which the clearness index is at least 0.66. What proportion of the days were clear?

• (HW_1_2) A sample of 26 offshore oil workers took part in a simulated escape exercise, resulting in the accompanying data on time (sec) to complete the escape ("Oxygen Consumption and Ventilation During Escape from an Offshore Platform." Ergonomics, 1997: 281-292). The escape times are shown below. The operators of the platform have requested your assistance in improving the platform. Specifically, the operators want to know what escape time corresponds with a 1% chance of being exceeded.

• How different are the sample mean and median?
• By how much should the largest time be increased so that the sample median is half the sample mean?

• (HW_1_3) The accompanying data on bearing load-life (million revolutions) for bearings of certain type when subjected to a 9.56 kN load are (Lubric. Eng., 1984, 153-159)

• What is the five-number summary for this data?
  
• Calculate the following sample measures of spread: variance, standard deviation and the mean-absolute-deviation.

• (HW_1_4) _{Run the virtual Roulette game 10 times (you can use the Spinner Experiment under the SOCR Experiments page http://socr.stat.ucla.edu/test/SOCR_Experiments.html, you must set the number of experiments, n=38)}. A Roulette wheel consists of 18 red, 18 black and 2 green spaces. The wheel is spun and a marble falls at random into one of the 38 spaces. Each sector in the Roulette wheel is numbered (0, 00, 1, 2, ..., 36).
  
  • Should all 38 possible outcomes occur the same number of times? Why?
  • Does it appear as if some outcomes are just too frequent and some are too rare?
  • How large is the difference between the even and odd outcomes in your 10 experiments? Is this expacted to vary for different students?
  • Would the answers to the above questions change if we did 1,000 experiments, instead of just 10?
    

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