The built-in data set, UKgas, is a time series recording the quarterly UK gas consumption from 1960 to 1986. Using R we

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The built-in data set, UKgas, is a time series recording thequarterly UK gas consumption from 1960 to 1986. Using R we canconvert this data into the vector x by the assignment x<-as.vector(UKgas). Assume that the n measurements x=(
x1, x2,...,xn
) are a random sample from a population with true unknownmean 𝜇 and true unknown variance
𝜎2
. Remember, x<- as.vector(UKgas)a) Calculate, n, the number of elements in x. b) Calculate the sample standard deviation s, of x. c) Estimate true mean 𝜇, using this data by calculating thesample mean. d) Calculate an unbiased point estimate of the populationvariance,
𝜎2
of UKgas. e) Assuming normality of UKgas data, calculate the maximumlikelihood estimate of 𝜇? f) Calculate the 65th percentile of x using R. g) Calculate a
trimmed mean for x using R. h) Since the sample size is >30 we can create a confidenceinterval for 𝜇 using a normal critical value. If we wantthe confidence interval to be at the 96% level and we use a normalcritical value, then what critical value should we use? i) Calculate a 96% confidence interval(using a normal criticalvalue) for 𝜇.(
,
)j) How long is the 96% confidence interval just created in parti? k) Copy your R script for the above into the text box here.