Homework 1 Due Date Time See Class Website 1 Answer the following questions as well as you can LATE HOMEWORKS ARE NEVER ACCEPTED You may meet consult with colleagues in the class But the assignment you turn in needs to be your own work Suppose That is X has a normal distribution with 30 and 2 144 1 1a 1b 1c 1d 2 2a 2b 2c 2d 2e 3 Find a transformation of that will give it a mean of zero and a variance of one ie standardize Find the probability that Supposing 5X find the mean of Find the variance of A bank has been receiving complaints from real estate agents that their customers have been waiting too long for mortgage confirmations The bank prides itself on its mortgage application process and decides to investigate the claims The bank manager takes a random sample of 20 customers whose mortgage applications have been processed in the last 6 months and finds the following wait times in days 5 7 22 4 12 9 9 14 3 6 5 8 10 17 12 10 9 4 3 13 Assume that the random variable measures the number of days a customer waits for mortgage processing at this bank and assume that is normally distributed Find the sample mean of this data Find the sample variance of Find the variance of For c d and e use the appropriate t distribution Find the 90 confidence interval for the population mean Test the hypothesis that is equal to 7 at the 95 confidence level Should you do a one tailed or two tailed test here What is the approximate p value of this hypothesis My nephew was born last summer He has 19 cousins on his father s side it s a big family I wish to know the mean of the distribution of the ages of my nephew s cousins which is the variable X I take a sample of 4 with ages and These are all drawn from the same underlying population Instead of calculating the sample mean of these four I do the following calculation to create an estimator of which I call 3a 3b 3c 3d 3e Explain what it means to say that is unbiased Show that is unbiased If the variance of is 15 what is the variance of If the variance of is 15 what is the variance of the Which estimator is more efficient the sample mean or Explain Homework 1 4 Suppose and Due Date Time See Class Website 2 4a If X and W are uncorrelated find the mean and variance of 4b Find the probability that Henceforth suppose that X and W have a correlation coefficient 25 4c What is the covariance of X and W 4d Find the probability that 4e Find the probability that 5 Our bank from Question 2 has decided to look more deeply into the matter of customer wait times In addition to information on the waiting times the bank has compiled information about the credit scores of the applicants That is the bank has 20 observation of the following 2 variables Observation 1 Wait Time 5 2 7 3 22 4 4 6 9 7 9 8 14 9 3 10 6 Credit Score 740 730 550 700 65 660 630 600 760 730 5 12 0 Observation 11 Wait Time 5 12 8 13 10 14 17 15 12 16 10 17 9 18 4 19 3 20 13 Credit Score 700 620 600 580 650 670 670 790 750 610 5a Find the sample mean and variance of the Credit Score variable you can call this variable Y if you like 5b Find the sample covariance and sample correlation coefficient of Wait Times and Credit Scores 5c Give a short interpretation of the correlation coefficient for this example 5d What story can you tell that would explain the correlation coefficient the bank observes