week 3

Week 3 : Data analysis, Modelling skills; 

1. Which of the following statements is true?

✅ Deterministic phenomena produce outcomes that can be predicted accurately.
❌ Random processes occur randomly.
✅ A process can produce a mix of deterministic and stochastic effects.
❌ Signals that are random can never take negative values.

2. What is / are the feature(s) of a deterministic signal?

❌ It is always periodic.
✅ Repeated experiments under controlled and identical conditions produce the same values.
✅ At any instant in time, there exists only one possible known outcome.
❌ Initial value is zero.

3. Identify the correct statement(s) among the following.

✅ Temperature of atmosphere 10 m above ground can be treated as random.
❌ Measurement of body temperature is deterministic.
✅ For a given data from a random process, there exists at least one observation less than the mean of observations in that data set.
❌ The population mean of a random variable is also necessarily random.

4. An estimator is said to be most efficient when

❌ The parameters can be estimated in the least possible time.
❌ The estimator provides accurate estimates with the smallest number of observations.
✅ Standard error in the parameter estimates is lowest when compared to that of all other estimators.
❌ It estimates parameters accurately even in the presence of outliers.

5. Identify the correct statement(s) among the following.

✅ Sample and ensemble averages are identical when the data obtained contains all possible outcomes.
✅ A statistic and estimator are both mathematical functions of the observed data.
✅ An estimate can have a large bias but low variability and vice versa.
✅ Accuracy is guaranteed when the estimation error vanishes by averaging across all possible data sets of fixed sample size.

6. Identify the correct statement among the following:

✅ Visualization of data is useful because it gives us an idea of any anomalies and trends in the data.
❌ Robust methods of estimation are meant to handle large amounts of missing values in the dataset.
❌ Estimates of parameters less than 10−410^{-4}10−4 can be neglected in any estimation exercise.
✅ Correlation between the pairs of variables in all four data sets given by Anscombe are identical.

7. Which of the following is true concerning variance of a parameter estimate?

❌ It is how the estimate varies from one method to another.
❌ Smaller values of parameter estimates have lower variance.
✅ Precision of an estimate is inversely proportional to its variance.
❌ Accurate estimators result in the lowest variability estimates.

8. Which of the following is true in data-driven analysis?

❌ Estimating the mean of a random variable is an example of predictive analysis.
❌ Exploratory analysis always deals with exploring which variable to measure.
✅ Performing a hypothesis test of zero correlation is an example of confirmatory analysis.
❌ Prescriptive analytics involves prescribing a particular method of data analysis.

9. Identify the incorrect statement(s) among the following:

✅ Estimating the mean of a signal is based on the same procedure regardless of whether the signal is deterministic or stochastic.
✅ Sample mean is the only means of estimating the mean of a stochastic signal.
✅ Expectation of a random variable and its sample average are identical.
❌ Transforming the data into another domain can be useful in visualizing the features of data.

10. Which of the following is true concerning a parameter estimate?

❌ It can be quite often equal to the true value.
✅ When averaged across a thousand data sets, the estimate can have lower error than that from a single record.
❌ The maximum value is obtained when the sample size is very large.
✅ The most efficient estimate is not necessarily the most accurate.