NPTEL 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 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 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 data set.
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 mean of a random variable is an example of predictive analysis.
Exploratory analysis always deals with exploring which variable to measure.
Performing 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.