- 1000 5 For Any I 1 1000 Let X Rayleigh O Denote The Predicted Wind Speed On A Random Day In The Future Let Y 1 (161.72 KiB) Viewed 72 times
1000 5. For any i = 1, .... 1000. let X Rayleigh(ô) denote the predicted wind speed on a random day in the future. Let Y' 1000 Li X be the predicted mean wind speed in the next 1000 days (assume that predicted individual wind speeds are independent of each other). Use simulation in R to estimate the distribution of Y'. Report this distribution by plotting a histogram and calculating numerical summaries. (Hint: Use the VGAM R package to get access to functions involving the Rayleigh distribution). [4 marks] 6. Climate researchers believe that in the comings years the variance of the wind speed will increase. Using the result of part (5), calculate the probability that this assumption is true based on the data and model available (i.e., calculate P[sd(Z') > sd(2)]. where sd(Z') is the standard deviation of the predicted sample of future wind speeds Z' = (X1,..., X1000) and sd (2) is the standard deviation of the sample x = (17... (1000)). 2, X ) Briefly comment on your results. [3 marks] 7. To assess if your conclusions are robust to errors in the estimation of o, recalculate the probability from part (6) by using the lower and upper estimates oL(2) and ou(2) derived in part (4). Briefly comment on your results.