Sample card prompts

• Under what dependency conditions does the linearity of expectation, [formula], hold?
• How is the variance [formula] expressed using the computational formula involving raw moments?
• Why is the divisor [formula] used instead of [formula] when calculating the sample variance [formula]?
• What is the formal definition of the bias of an estimator [formula]?
• How does the covariance [formula] relate to the product of expectations when [formula] and [formula] are independent?
• Which mathematical inequality ensures that the correlation coefficient [formula] is always bounded between [formula] and [formula]?
• What specific property of the normal distribution allows the standardizing transformation [formula]?
• Under what specific distributional assumption does zero covariance between two variables imply their absolute independence?
• According to the Central Limit Theorem, what is the distribution of the standardized sum of [formula] independent and identically distribute
• How does the standard error of the sample mean [formula] scale with the number of observations [formula]?
• Into which two components can the Mean Squared Error (MSE) of an estimator be decomposed?
• What is the formula for the conditional variance of [formula] given [formula] in a bivariate normal distribution with correlation [formula]?

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