Mathematical Modeling by Linear Algebra (4 problems)
#1-2: Exercise 5.8. (This problem was assigned in the last set of homework. You are asked to read my solution and redo this problem with my csv data from BB and with your improved R codes with your own style. Again, this problem is long and is considered as two problems): The monthly dataset is NOAAGlobalT.csv. You need to extract the data for the Pacific region first, and then convert the monthly data in annual data. Then you can apply the SVD command.
#3-4: Exercise 5.9 (This problem is long and is considered as two problems): The dataset is PrcpRecon5degAnn.csv,
Mathematical Modeling by Calculus (3 problems)
#5: Exercise 6.1
#6: Exercise 6.5
#7: Exercise 6.6
Probability Modeling
#8: (a) Derive the Buffon’s needle problem solution when the needle length is longer than the gap of two lines.
(b) Write an R program to simulate the above Buffon’s needle problem in (a).
#9: Write an R code for Monte Carlo simulation to calculate the volume of a unit ball in 8-dimensional space.
#10: When one roll two dice randomly, it is known that the event of two dice’s sum equal to 7 has a probability 1/6. Write an R code to simulate this process and verify this result.
follow the syntax of the book for the coding part
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