Recall the rules for means and variances of independent random variables.

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BlackTom AI · Accepted Answer

The question asks us to Recall the rules for means and variances of independent random variables.
Option 1: The first option is an empty string, so there is no statement to evaluate. Since there is no content here, it cannot be judged as true or false, and we cannot assign any meaning to it in the context of the rules.
Option 2: The second option is also an empty string, providing no information to assess. Like Option 1, there is nothing to analyze or compare against known rules.
Option 3: The third option is likewise an empty string, offering no content for evaluation. It cannot be used to support or contradict the standard rules.
In this case, the provided answer (σ²x + σ²y) aligns with the well-known rule for the variance of the sum of independent random variables: Var(X+Y) = Var(X) + Var(Y) = σ_x^2 + σ_y^2. This is the correct form for the variance rule in the independent case, but because the listed options are all empty, there is no explicit option to match this statement to. The presence of the explicit correct expression in the answer field indicates the expected result, even though the answer options themselves do not reflect it.
Overall, the key concept is that for independent variables, variances add when you sum the variables, i.e., Var(X+Y) = σ_x^2 + σ_y^2. The empty options fail to present any evaluative statements to choose from, making it impossible to select the correct option from the given list.

ECON 3640-090 Spring 2025 Lecture #14 Warm-Up

Recall the rules for means and variances of independent random variables.

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