The built-in data set, UKgas, is a time series recording the quarterly UK gas consumption from 1960 to 1986. UsingR we can convert this data into the vector x by the assignment x<-as.vector(UKgas). Assume that the nmeasurements x=( X₁, X2,...,xn) are a random sample from a population with true unknown mean μ and trueunknown variance ². Remember, x<- as.vector(UKgas)a) Calculate, n, the number of elements in x.b) Calculate the sample variance of x.c) Estimate true mean μ, using this data by calculating the sample mean.d) Calculate the sample standard deviation,s, of xe) Assuming normality of UKgas data, calculate the maximum likelihood estimate of μ?f) Calculate the 70th percentile of x using R.g) Calculate a108trimmed mean for x using R.h) Since the sample size is >30 we can create a confidence interval for u using a normal critical value. If we wantthe confidence interval to be at the 94% level and we use a normal critical value, then what critical value should weuse?i) Calculate a 94% confidence interval(using a normal critical value) for μ.j) How long is the 94% confidence interval just created in part i?

By bartleby policy i can gives only 3 subparts answer at a timme Here we have to use R-code UKgas…

Answered: The built-in data set, UKgas, is a time…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The maximum patent life for a drug is 17 years. Subtracting the length of time required by the FDA for testing and approval of the drug provides the actual patent life for the drug that is, the length of time that the company has to recover research and development costs and to make a profit. The distribution of the lengths of actual patent lives for new drugs is given below, where Y is a random variable representing actual patent life of a drug (in years): y P(Y=y) F(y) 4 5 6 7 8 9 10 11 0.06 0.08 0.11 0.15 0.22 0.18 0.12 0.08 a) Complete the table above with the cumulative probability distribution for actual patent life (F(y) = P(Y ≤ y)). b) What is the probability that the actual patent life of a random drug is 6 years or less? c) What is the probability that the actual patent life of a random drug is more than 8 years? Show this in two ways: i. using the probability distribution for Y ii. using the cumulative probability distribution for Y, and applying our probability of comple-…
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