Ex. I. Setup: Data XI, xn i.i.d. from Exponential (theta) where EX=theta-0 and V

Question

Ex. I. Setup: Data XI, xn i.i.d. from Exponential (theta) where EX=theta-0 and Var (X)- ltheta 2. Ex. 2. Setup: Data X.,Xn i.i.d. from Normal (Itheta, 4). Ex. 3. Setup: Data X.Xn i.i.d. from Normal (0, lsigma*2); Itheta-sigma*2, i.e., the variance Ex. 4. Setup: Data X,.Xn i.i.d. from Normal (0, Isigma 2); Itheta-sigma>0, i.e., the standard deviation. Let n-100. In all cases, assume that you observed a sample mean equal to 5 and a sample variance (using n-1 in the denominator) equal to 9. For Exercises 1-4 : construct a 95% confidence interval for parameter theta using the asymptotic distribution of the MLE with variance given by the inverse of Fisher information. .*.94 1.1

Explanation / Answer

Let Theta =1

data1=rexp(n=100,rate=theta)

data2=rnorm(n=100,mean=theta,sd=2)

data3=rnorm(n=100,mean=theta,sd=sqrt(theta))

data4=rnorm(n=100,mean=theta,sd=theta)

95 percent Confidence intervals = [3.89,6.10]

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