Question

Let X have a Normal distribution with mean μ and variance σ² . In this problem, the Fisher Information is for 1 random variable (or random sample). Assume μ is unknown and σ² is known. Find the Fisher Information I(μ).

Answer 1

The Fisher Information I(μ) for a normally distributed random variable with known variance and unknown mean is the inverse of the variance, given by I(μ) = 1/σ².

Step-by-step explanation:

The student is working on a problem from the field of statistics which involves finding the Fisher Information for a normally distributed random variable X with mean μ and known variance σ² where μ is unknown. When dealing with Fisher Information, the formula to use is I(μ) = 1/σ² as it is the inverse of the variance for a single observation from a normal distribution with known variance. This measure of information quantifies how much information a random variable X contains about an unknown parameter μ.

The calculation of Fisher Information is commonly used in maximum likelihood estimation and in constructing confidence intervals and hypothesis tests within the context of statistical inference.