Question

Assume that X is an independent random variable with mean, μ and variance, and variance, σ²

Say if each statement if TRUE or FALSE -- if FALSE, rewrite so it's correct.
1. We generally use σ² to denote an estimator of μ.
2. We often use θₙ to denote a generic estimator and θ to denote a generic estimand.

Answer 1

The statement that σ² is used to denote an estimator of μ is false; σ² denotes the variance of a population. The statement about using θₙ for an estimator and θ for an estimand is true.

Step-by-step explanation:

Let's evaluate the statements about statistical estimators and parameters given an independent random variable X with mean μ and variance σ².

1. We generally use σ² to denote an estimator of μ. FALSE. This statement is incorrect because we use σ² as the notation for the variance of a population, not as an estimator for the mean (μ). The correct statement would be: We generally use μ to denote the mean of a population, and σ² to denote its variance.

2. We often use θₙ to denote a generic estimator and θ to denote a generic estimator. TRUE. This statement is correct. θₙ is commonly used to represent an estimate of a parameter, while θ represents the parameter itself that is being estimated.