Use R statistical software to answer the following: 2. Let x1 , ..., xn be a...

Question

Question

Use R statistical software to answer the following:

2. Let x1 , ..., xn be a random sample from the normal distribution with mean 0 and variance θ.

(a) Find the mle of θ

(b) Find the Fisher information I(θ)

Answer 1

Answer #1

A) We know that if X is random varible with N(0,theta) then

MLE for theta

Thus R code is:

X={.....} # Observed vector
MLE=(1/length(X))*sum(X^2)
MLE

B) Also if X is random varible with N(0,theta) then

Fisher information I(theta)

where, S^2

Thus R code is:

X={.....}
S=(1/length(X))*sum(X^2)
FI= (length(X)/2)*S^4
FI # Fisher information

Answer 2

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