What is the probability that there are at most 2 car accidents reported thought a month?

Economics by Geoffrey

Provide solutions to any 10 questions and ignore one question at your wish.

 

Generate the daily growth rate as: g_XXX = XXX/XXX[_n-1]  – 1

 

 

Question 1: Generate Growth Indicator gi_XXX as follows:

 

gi_XXX = -2 if g_XXX is smaller than -2%

gi_XXX = -1 if g_XXX is between -2% and 0%

gi_XXX = 1 if g_XXX is between 0% and 2%

gi_XXX = 2 if g_XXX is larger than 2%

 

and draw a pie chart showing the values and frequencies of gi_XXX.

 

Answer to Question 1:

 

 

 

Question 2: What are 1st, 2nd, 3rd quartiles and the IQR of gi_XXX defined above?

 Answer to Question 2:

 

Question 3: The probability that an insurance company will declare bankruptcy on a given business date is 0.001. What is the probability that the insurance company will survive bankruptcy for the next 250 business days?

 

 Answer to Question 3:

Question 4: The insurance company receives insurance claims on average 2 per business day. What is the probability that the insurance company will receive exactly 7 claims through the next 5 business days? 

Answer to Question 4:

 

Question 5: On a given day, there is a car accident reported at the intersection of victory Blvd and Richmond Avenue with a probability 0.05. What is the probability that there are at most 2 car accidents reported thought a month?

Answer to Question 5:

 

Question 6: John and Linda are working on a homework assignment. The amount of time in minutes John completes his assignment is uniformly distributed between 35 and 55 minutes, inclusive. While the amount of time in minutes Linda completes her assignment is uniformly distributed between 25 and 45 minutes, inclusive. What is the probability that Linda completes her assignment earlier than John does? (Please provide a STATA code, and STATA table, and justify your answer!)

 

Answer to Question 6:

Question 7: Anna, Sandra, and Jessy take Graduate Management Admission Council’s GMAT examinations. Their scores on the GMAT are roughly normally distributed with a mean of 527 and a standard deviation of 90. What is the probability that Anna obtains the highest grade?

 

Answer to Question 7:

Question 8: There are i = 1,2,3,4,5 classmates who run a marathon. Time in minutes that a player finishes a marathon is uniformly distributed between 25 – i minutes and 25 + i minutes. Let Xi denotes the time player i = 1,2,3,4,5, needs to complete the marathon. Let denotes the average number of time needed to complete the marathon. What is the standard deviation of ? (Please provide a STATA code, and STATA table, and justify your answer!)

Answer to Question 8:

Question 9: Let p denotes the probability that the stock price declines more than 2% on a given day. At 95% confidence, test the null hypothesis H0: p >= 60%, against the alternative Ha: p < 60%. Please provide the STATA code, and STATA table, and explain your answer.

 

Answer to Question 9:

Question 10: Let p1 and p2 denote the probability that the stock prices (1st and 2nd tickers you are assigned with) increase by more than 3%. At 95% confidence, test the null hypothesis H0: p1 = p2, against the alternative Ha: p1 != p2. Please provide the STATA code, and STATA table, and explain your answer.

 Answer to Question 10:

Question 11: Ind1 = 1 or -1 depending on whether the stock (1st ticker you are assigned with) increases more than 1% on a given day and let Ind2 = 1 or -1 depending on whether the stock (2nd ticker you are assigned with) increases more than 1% on a given day.

Test the following hypothesis

H0 : Ind1 & Ind2 are independent vs Ha: Ind1 & Ind2 are dependent?

Answer to Question 11: