CAIIB Paper 1 Module A Quiz 9

The standard error of the mean is σ/√n = 12/√36 = 12/6 = 2. It measures the sampling variability of the sample mean.

The median depends on the order position rather than the magnitude of an extreme observation, so it is generally more robust to outliers than the mean.

Least squares chooses the fitted line that minimises the sum of squared residuals, the squared differences between actual and fitted values.

For a Bernoulli variable, variance = p(1−p) = 0.2×0.8 = 0.16.

Quantities produced or resources allocated generally cannot be negative, so decision variables are restricted to values ≥0 unless the problem explicitly permits signed values.

Weighted rate = (10×6% + 30×8%)/(10+30) = (0.6+2.4)/40 in lakh-rate units = 7.5%. Weights are deposit amounts.

Sampling error is the difference between a sample statistic and the population parameter due to observing a sample rather than the entire population.

With an even number of periods in the moving-average span, the calculated average falls between time points; centring aligns it with a particular quarter.

Independent replications help estimate simulation variability and uncertainty, allowing confidence intervals or error estimates for reported outputs.

Sensitivity analysis studies the effects of changes in objective coefficients, resource limits or other model parameters on the optimal solution and objective value.

For a normal population, the sample mean is normally distributed for any sample size, assuming independent random sampling.

The coefficient of variation expresses standard deviation relative to the mean, making it useful for comparing relative variability across series with different scales, provided means are positive and meaningful.

A forecast should account for recurring seasonal effects as well as trend where relevant. Ignoring a stable seasonal pattern can systematically misstate demand.

VaR at a 99% confidence level estimates a loss threshold that should not be exceeded on about 99% of days under the model and assumptions. It does not describe the size of losses beyond that threshold.

An infeasible model has no point that satisfies all constraints simultaneously; the constraints conflict with one another.

Adding a constant shifts every observation and the mean equally, leaving deviations from the mean unchanged. Therefore standard deviation is unchanged.

Deliberately false responses are a non-sampling error; such errors can occur even in a census and are not removed simply by increasing sample size.

Exponential smoothing applies weights that decline exponentially for older observations, so recent values generally have greater influence.

Verification asks whether the computer implementation correctly represents the conceptual model; validation asks whether the model adequately represents the real system for its intended purpose.

Extreme simulated outcomes may be important tail risks. They should be investigated for model plausibility and retained unless there is a defensible reason to treat them as errors.